G: Yes. I think there are several conceptually distinct ways to do this, and the important thing is not to decide in advance that every unwavering presidential supporter is lying or irrational. What you actually want to estimate is something like a presidential-response bias: how much of the observed answer is attributable to the respondent's evaluation of the underlying event, versus a rule they apply because the actor is their president or the President.

The cleanest approaches I can think of are these.

1. Actor-blind polling. Describe the conduct without identifying the president, party, or administration, then ask whether the conduct is acceptable. Later, after enough intervening questions, ask the same respondent's presidential approval and partisanship. You can then compare, say, people who approve of Action X when it is anonymous with people who approve after learning that their preferred president did it. That difference is measurable presidential/partisan elasticity.

2. Randomized actor substitution. Randomly assign respondents otherwise identical scenarios: "President Trump did X," "President Biden did X," "a Democratic president did X," "a Republican president did X," or simply "the president did X." Now you've created something much stronger than ordinary polling. If someone says X is unacceptable under the opposing president but acceptable under their own, you can measure the actor effect directly. At the population level, this gives you an experimentally estimated partisan correction rather than an assumption about who's being obtuse.

3. Counterfactual consistency questions. Ask the substantive question and then something like: Would your answer be the same if a president of the other party did exactly the same thing? I wouldn't simply trust the answer to that second question, though. Better would be to actually present several mirrored cases elsewhere in the survey. The discrepancy between the mirrored answers becomes a respondent-level consistency measure.

4. Presidency-versus-person separation. This gets directly at your second category. Ask separately whether respondents think (a) the action was good, (b) the president deserves support, and (c) Americans should publicly support the president even when they believe he is wrong. Somebody answering "bad action / support president / yes" is telling you something quite different from "good action / support president." The first is displaying institutional or patriotic deference, while the second may genuinely approve of the conduct.

5. Approval ceilings and floors. Instead of treating presidential approval as an ordinary 0–100 variable, repeatedly measure it across radically different hypothetical conditions: "What, if anything, could make you disapprove?" and the reverse for committed opponents. You may discover a subgroup whose probability of approving is effectively bounded below at, say, 95%, irrespective of inputs. Statistically, I'd treat that as a structural approval floor, rather than pretending every response represents a fresh evaluation of presidential performance.

6. Within-person normalization. This may be closest to what you're imagining by "normalize." Give respondents a battery of presidential actions ranging from mundane to extreme, with randomized party/identity information. Estimate each respondent's baseline tendency to favor their side. Then report both the raw result and an adjusted result: roughly, observed evaluation minus estimated actor/partisan effect. You wouldn't literally subtract 15 points from every Trump supporter or Democrat; you'd estimate the distortion probabilistically from that respondent's behavior across the battery.

There is also a particularly interesting implementation if the target is public reluctance to criticize the presidency itself. Ask the identical substantive question in two forms: one asks what the respondent thinks; another asks what advice they would give the president privately; a third asks what they would say publicly. Someone answering "wrong / tell him privately that he's wrong / publicly support him" has practically identified the response mechanism for you. That's not ordinary approval at all. You're measuring a social norm governing expression.

And I would resist producing just one "corrected presidential approval number." The much more informative result would look something like:

Raw approval: 47%
Policy/conduct approval when actor is blinded: 39%
Estimated partisan actor premium: +6 points
Estimated presidential-deference premium: +2 points

Those hypothetical numbers would tell us something that "47% approve" completely destroys through information flattening.

The methodological trick underlying all of these is that you don't identify the biased population by asking them whether they're biased. You create situations in which the bias has something to push against. Once the underlying conduct, presidential identity, party identity, publicity, and institutional loyalty are independently varied, the previously invisible constant becomes an estimable variable.

And I suspect your "particular restrictions" may be going toward an especially useful version of this: defining circumstances under which an answer becomes non-informative rather than simply calling it wrong. If someone literally cannot give the president a negative evaluation under some defined range of conditions, their answer still tells you something important about loyalty, but it contains very little information about performance. Those are two different variables that conventional approval polling unfortunately compresses into one.

G: [Non-text content: thoughts; content_type=thoughts]

G: I think your election-number instinct is useful, but I’d use it as a calibration anchor for the partisan floor, not as a direct substitute for approval. The trick is separating “people who chose him” from “people whose approval is effectively locked to him.”

G: [Non-text content: thoughts; content_type=thoughts]

G: [Non-text content: reasoning_recap; content_type=reasoning_recap]

G: Yes. I think the election result can be made mathematically useful in almost exactly the way you're describing: not as another poll to average in, but as the center-point that tells you how much politically available support existed at the beginning.

For 2024, Trump received 49.80% of the presidential vote and Harris 48.32%. citeturn169249search12turn169249search13 So for a Trump second-term series, I'd initially define 49.8 as the electoral baseline, rather than treating 50% approval as some naturally meaningful center.

Then build the normalization around three points:

[ L = \text{effective approval floor} ]

[ E = \text{election support baseline} ]

[ U = \text{effective approval ceiling} ]

The useful transformation would be piecewise, because movement below the electoral baseline means something different from movement above it:

[ N(A)= \begin{cases} 50\frac{A-L}{E-L}, & A\le E\ 50+50\frac{A-E}{U-E}, & A>E \end{cases} ]

That has a very attractive interpretation:

0 = essentially everyone capable of abandoning him has abandoned him.
50 = his election coalition is intact.
100 = essentially everyone capable of being won over has been won over.

That is much closer to what I think you're trying to communicate than ordinary approval.

Why the election result helps

Suppose, purely illustratively:

• electoral baseline (E=49.8)
• immovable approval floor (L=32)
• immovable disapproval means effective ceiling (U=94)

Now a 38% approval isn't represented as "38 out of 100," which psychologically looks vaguely near the middle.

Instead:

[ 50\times\frac{38-32}{49.8-32}\approx16.9 ]

So his normalized score would be about 17/100.

That says something much more intuitively meaningful:

Of the support that was actually available for him to lose after winning the election, roughly 83% of it has been lost.

Not 83% of his voters, importantly. Eighty-three percent of the distance between his electoral coalition and his estimated irreducible support floor.

And notice why this gets interesting with Trump's current numbers. Reuters/Ipsos had him at 35% approval on August 3, 2026, one point above the lowest approval Reuters/Ipsos had recorded for his presidency. citeturn922398news34 Gallup's historical series puts his first-presidency low at 34%, and Gallup recorded 36% in December 2025. citeturn922398news4turn922398search11 So your intuition about a stubborn region somewhere in the 30s is empirically quite understandable, although we'd want to derive the floor rather than simply decree "34."

And this is where I think your election idea solves part of the partisan problem.

Don't estimate the partisan floor from approval alone

I'd decompose the floor:

[ L=P+R ]

where (P) is a presidential/institutional floor—people predisposed to approve of virtually any sitting president—and (R) is the president's partisan locked floor.

Your first category can be estimated historically across presidents. Look at the tails of extraordinarily unpopular presidents of both parties and ask how much approval stubbornly remains. Gallup gives lows such as Nixon 24%, George W. Bush 25%, Carter 28%, George H.W. Bush 29%, Trump 34%, Biden 36%, etc. citeturn922398search11 You wouldn't simply average those because the political environment changed enormously, but they give you material for estimating the structural bottom.

For the partisan component, however, I'd introduce the election:

[ R=E\times c ]

where (c) is the estimated coalition lock coefficient.

That's the quantity you're really after.

If someone got 49.8% of the vote and historical/cross-tab evidence suggests that perhaps 65% of that electoral coalition behaves as effectively non-responsive presidential approvers, then:

[ 49.8\times .65=32.4 ]

You've just derived a 32.4-point partisan floor from the electoral coalition rather than saying, "Well, his approval seems never to drop below 32."

And there is real evidence for modeling something like (c). Modern approval has become extraordinarily partisan. At the beginning of Trump's second term Gallup found 91% Republican approval versus 6% Democratic approval; Biden began at 98% Democratic and 11% Republican approval. Gallup says this degree of partisan polarization is characteristic of the modern period rather than uniquely Trump-specific. citeturn922398search10turn922398search13

So I would make the first crude model:

[ \boxed{L=P+(E-P)c} ]

rather than simply (E c), because you don't want to count the generic presidential-loyalty group twice.

And similarly at the other end:

[ \boxed{U=100-[Oq]} ]

where (O) is the opposition electoral coalition and (q) is its locked-disapproval coefficient.

That creates exactly the symmetry you were talking about. Somebody who will never approve isn't evidence that the president failed to persuade them this month, any more than somebody who will always approve is evidence that he succeeded.

There's another way of using the election that I think may actually be even better for communication.

Make Election Day = 100 coalition units rather than 50 on a 0–100 ideological scale.

Trump begins with:

[ 49.8%=100\text{ support units} ]

If his irreducible floor is estimated at 32%:

[ 32%=0\text{ defeasible-support units} ]

Then 38% becomes:

[ \frac{38-32}{49.8-32}\times100\approx34 ]

So instead of saying:

Trump approval: 38%

you could say:

Coalition retention: 34%

Meaning that only about one-third of the approval that could realistically disappear from his winning coalition remains above the modeled partisan floor.

I think that is very close to your interest-rate analogy. 38% sounds like 38/100 because the human brain automatically supplies zero as the denominator. But politically, zero isn't actually available. If perhaps 30-something percent is effectively inaccessible because of partisan/institutional loyalty, then the behaviorally available scale isn't 0–100. It's something closer to 32–94 or whatever the historical analysis establishes.

The normalization's job is therefore not to claim those 32 people "don't count." They absolutely count electorally. It's to say:

They no longer contain much information about marginal changes in presidential performance.

That's the distinction I think makes the whole exercise defensible.

And there is one particularly nice property of using election support as the midpoint rather than choosing an arbitrary "normal approval" figure: the calculation automatically adjusts for presidents with different mandates. A president elected with 42% of the vote and one elected with 58% don't start from the same political coalition. Their subsequent 38% approval ratings therefore shouldn't necessarily mean the same thing.

So I think your "first iteration of the curve" is sound. Election result establishes the initial coalition; historical approval behavior estimates how much of each coalition is immovable; the remaining interval is stretched to fill the usable 0–100 range. Then, in later iterations, you could make (c) and (q) dynamic by era, partisan polarization, election type, turnout, and perhaps strength of partisan identification rather than pretending they're universal constants.

That gets you away from the very misleading intuition that 35 is "only fifteen points below half." On a suitably normalized political-response scale, 35 could quite reasonably represent something like 10 or 15 out of 100, because most of the apparent space underneath it was never politically traversable in the first place. memcite

G: [Non-text content: thoughts; content_type=thoughts]

G: [Non-text content: reasoning_recap; content_type=reasoning_recap]

G: Yes — and first, the 65% I used before was purely illustrative. I did not pull it from a dataset. I should have marked that more aggressively, because in the model we're discussing that coefficient would eventually have to be estimated rather than casually supplied.

More importantly, I think I now see the distinction you're making between the absolute election share and the margin, and I agree that they are measuring different things.

Trump's 2024 popular-vote share was about 49.8%, Harris's about 48.3%, so the margin between them was about 1.5 percentage points. citeturn832789search0 Your intuition is that this 1.5 isn't merely trivia about who won. It is evidence about how narrowly divided the politically activated electorate was at the moment the presidency began.

That's different from saying "Trump started with 49.8%."

Those two numbers encode different information:

• 49.8% tells us the size of Trump's actual voting coalition.
• +1.5 points tells us the coalition's advantage over the alternative coalition.

And I think you're right that using only the first potentially loses something important.

Imagine two presidents:

President A wins 58–40.

President B wins 49.8–48.3.

Both subsequently have 42% job approval.

If we normalize only against their own vote shares, A has fallen 16 points and B has fallen 7.8. That's meaningful.

But it misses something else: President A entered office with an enormous amount of demonstrated relative public advantage. President B entered with almost none.

President B's election result is basically telling us:

The country was already balanced almost exactly on the partisan fulcrum when this presidency began.

That's valuable information for precisely the normalization you're constructing.

Where I think my previous model got ahead of yours

You're also correct about L, the floor.

I initially said, approximately:

[ L = P + R ]

with (P) being generic presidential/patriotic loyalty and (R) being partisan locked support.

That's conceptually fine.

But I then moved too rapidly toward estimating (L) from observed low approval ratings.

Your objection is correct: an observed historical low is not the thing we're trying to estimate.

It is:

[ \text{Observed Low}

\text{Patriotic Floor} + \text{Partisan Floor} + \text{Actual Persuadable Approval still remaining} ]

And possibly other effects.

So if Nixon bottoms at 24%, for example, we cannot say "24% is the presidential floor." Gallup does indeed record Nixon at 24%, George W. Bush at 25%, Carter at 28%, and so forth, but those are observations, not clean measurements of the latent "will always approve" population. citeturn832789search0

That's exactly the contamination problem you're pointing out.

This is where older data become especially useful

And I now understand why you're deliberately interested in pre-hyperpartisan data, rather than thinking that older data are merely an inferior version of modern data.

You're trying to identify the components before they became badly entangled.

Gallup's long-run data actually support your premise that modern partisan presidential response is different in degree. Gallup found that the ten most polarized presidential years in its series through 2020 had all occurred within the preceding sixteen years. For Trump's third year, Republican approval averaged 89% while Democratic approval averaged 7%. Earlier presidencies had partisan differences, of course, but they generally weren't this mechanically extreme. citeturn832789search5

So historical data could be used somewhat like a laboratory with a cleaner mixture.

You don't ask:

"What was Truman's lowest approval, therefore that's the patriotic floor?"

Instead you examine many older presidents and try to infer:

"When party identification exerted substantially less control over presidential approval, what portion of the electorate nevertheless seemed resistant to saying either 'I disapprove of the president' or 'I approve of the president'?"

That gets closer to your generic always-positive / always-negative component.

Then modern data tell us how much additional distortion appeared when party identity became much more tightly coupled to presidential approval.

That is a much better conceptual separation.

Now to the election margin.

I think the cleanest first iteration would preserve both vote share and margin instead of forcing one to replace the other.

Let:

[ V = \text{winner's vote share} ]

and

[ M = V_{\text{winner}}-V_{\text{runner-up}} ]

For Trump 2024, approximately:

[ V=49.8 ]

[ M=1.5 ]

These answer two separate questions.

V: How large was the president's demonstrated coalition?

M: How much demonstrated advantage did that coalition possess over its principal alternative?

And the second becomes especially revealing when neither candidate gets 50%.

Suppose:

Election X: 58–40 → margin 18.

Election Y: 50.75–49.25 → margin 1.5.

Election Z: 46–44–10 → margin 2.

Y and Z have similar margins, but they are clearly not equivalent elections. In Y, virtually everybody chose one of the two principal candidates. In Z, fully 10% of voters rejected both.

That's why I think you were having trouble completing the thought about absolute numbers being vulnerable to other variables. Margin fixes one problem but introduces another if used alone.

The margin knows how close the top two were.

It does not know how much of the electorate they jointly captured.

So I'd introduce one more exceedingly simple number:

[ C=V_1+V_2 ]

Call it, provisionally, major-candidate concentration.

For Trump/Harris:

[ C\approx98.1% ]

That means the 1.5-point margin occurred in an election where almost the entire presidential vote was divided between those two choices. That's quite different from a 1.5-point victory in a three-way election where the top candidates only collected, say, 75% combined.

So now we've got three pieces of election information without doing anything fancy yet:

[ \boxed{V,\ M,\ C} ]

V — coalition size

M — relative electoral advantage

C — how completely the election was actually divided between those coalitions

And I think this gets remarkably close to the "first approximation of the curve" you were reaching for.

Why margin could matter enormously for normalization

Here's the thought I think you were circling.

If a president wins 58–40, then some portion of his initial coalition cannot plausibly be explained merely by the ordinary partisan divide. He won people beyond the point of political equilibrium.

Whereas if somebody wins 49.8–48.3, almost the entire election result could theoretically be produced by two highly stable opposing political blocs plus a tiny group that determines the outcome.

That's crucial.

In the first case, election support itself provides evidence of cross-cutting persuasion.

In the second case, election support provides much weaker evidence of that.

So instead of treating:

[ V = 49.8 ]

as 49.8 points of equally informative presidential support, we could eventually decompose it as:

[ V = B + X ]

where:

(B) = baseline/structural coalition support

(X) = marginal or genuinely contestable support.

And margin is one possible empirical clue for estimating X.

A landslide winner necessarily has a lot of (X).

A razor-thin winner may have very little.

That may be the missing connection you were trying to articulate.

There's also an important historical wrinkle supporting the usefulness of this approach. Presidential approval itself has not behaved on a fixed 0–100 psychological scale. Gallup's long record includes presidents with highs of 80–90% and lows in the 20s, while Trump's first term occupied the unusually compressed range of roughly 34–49%. citeturn832789search0 That's exactly the phenomenon you're trying to correct: the raw scale still says 0–100, but the politically reachable scale has become much narrower.

And Gallup separately found that perceptions of presidents have become heavily party-conditioned; even retrospective evaluations show large party gaps for Reagan, Clinton, Bush and Obama, while some earlier presidents produce far smaller divisions. citeturn832789search3turn832789search4

So I would now alter our sequence of operations.

Don't start with Trump's 35 or 38 and ask, "What floor makes this meaningful?"

Start historically and build the latent scale:

[ \text{Raw approval}

\text{structural presidency effect} + \text{partisan lock} + \text{contestable judgment} ]

Then use historical polling to estimate the first component, electoral results—including both vote share and margin—to constrain the second, and finally treat what's left as the politically responsive component we're actually interested in stretching back onto 0–100.

That has one feature I particularly like for your purpose: Trump doesn't define the normalization.

You construct the measuring instrument from Eisenhower through Biden—or perhaps from whichever historical period gives us sufficiently comparable data—and then put Trump into it.

If Trump turns out to break the instrument because modern negative partisanship behaves differently from older positive partisanship, that's an empirical discovery about Trump-era politics rather than something baked into the formula.

And that is probably where I would go next: actually take perhaps Eisenhower onward, collect election winner share, election margin, combined major-party share, presidential approval high/low/average, and see whether the pre-polarization presidents reveal a relationship between electoral margin and the traversable approval range. We could then see what kind of normalization emerges before deliberately introducing the Trump/Obama/Biden hyperpartisan period as a stress test rather than using it to design the model. memcite

G: Yes. I think you've now sharpened the dependent variable considerably. "Disapproval" isn't really what this instrument would measure. Something like disenchantment is much closer.

Ordinary approval asks:

What fraction of Americans approve of the president now?

What we're constructing asks something more like:

How much of the politically contingent support available to this president has been lost, after removing support and opposition that appear structurally insensitive to presidential performance?

That is a different quantity.

And it makes Nixon unusually interesting.

Nixon as a possible empirical floor event

I wouldn't initially define Nixon's 24% as the patriotic floor. I'd do something methodologically more useful: treat Nixon as a candidate saturation event.

In other words, our hypothesis would be:

[ \text{Nixon}_{1974}\approx P + R + \epsilon ]

where:

• (P) = presidency/patriotic floor,
• (R) = remaining partisan floor,
• (\epsilon) = whatever persuadable support survived Watergate.

Your stronger hypothesis is that both (R) and (\epsilon) may have become unusually small. If that's borne out, then:

[ \text{Nixon}_{1974}\approx P ]

And that would be extraordinarily valuable.

The historical circumstances make him particularly useful because the mechanism of collapse was not merely "people don't like the economy" or "the war is unpopular." Watergate attacked something much closer to the credibility of the presidency itself, culminating in Nixon losing congressional Republican support as the evidence accumulated.

So Nixon gives us something George W. Bush's 25% doesn't necessarily give us even though the raw numbers are almost identical.

That's actually an excellent demonstration of why min(raw approval) isn't sufficient.

[ Nixon=24 ]

[ Bush=25 ]

does not imply:

[ \text{latent political state}{Nixon}\approx\text{latent political state}{Bush} ]

Bush's 25 could contain a substantial number of ordinary Republican voters who continued to think he was doing an acceptable job. Nixon's 24 could conceivably be much closer to people who would not tell a pollster they disapproved of the sitting president almost irrespective of circumstances.

Same observed output. Potentially very different mixtures underneath.

And your pre-2016 restriction is exactly how I'd do the experiment

I'd actually freeze that as a methodological rule before looking at results:

Development set: Eisenhower through Obama, with observations ending before the 2016 election.

Out-of-sample stress test: Trump I → Biden → Trump II.

That's better than allowing post-2016 observations to influence the coefficients and then announcing that the model shows something changed after 2016. That would partially bake the thing we're trying to discover into the measuring device.

And there's another benefit. We don't actually have to assert at the beginning that 2016 broke presidential polling.

Our weaker hypothesis can simply be:

A model fitted to the earlier presidential system should continue describing later presidencies if the underlying relationship between electoral support, partisan attachment and presidential approval remains substantially unchanged.

Then run Trump through it.

If it works, interesting.

If it fails, the pattern of failure becomes the result.

For example, imagine our pre-2016 model predicts that a president experiencing conditions corresponding historically to a normalized disenchantment of 85 should have raw approval around 24–27%, but Trump persistently sits at 35–39%.

That residual:

[ \text{Observed Approval}-\text{Expected Approval} ]

becomes extremely interesting.

We don't have to call it "cultism" or "hyperpartisanship" or anything else in the mathematics. We have discovered an unexplained support premium that the historical model cannot reproduce.

Then we investigate what explains it.

That is much cleaner.

"Disenchantment" also solves an important semantic problem

I particularly like your distinction because disenchantment doesn't require identical expectations.

Suppose Reagan voters expected smaller government, Carter voters expected competent technocracy, Obama voters expected post-partisan reform, and Trump voters expected disruption.

Those expectations aren't commensurable as political goals.

But they are potentially commensurable in another sense:

[ \text{Expected presidency}\rightarrow\text{Experienced presidency}\rightarrow\text{support retained/lost} ]

We don't need to decide whether the original expectation was intelligent, realistic, moral, coherent, etc.

We're measuring departure from the support state demonstrated when the electorate selected the president.

So perhaps the central quantity eventually becomes something like a Presidential Disenchantment Index (PDI).

I'd orient it intuitively:

[ PDI=0 ]

means essentially no measurable disenchantment from the president's contingent electoral support, while

[ PDI=100 ]

means essentially all support that historically behaves as persuadable has disappeared.

Then Nixon 1974 might turn out to be something like 96 or 100—not because we decree that Nixon represents maximum possible awfulness, but because the historical data indicate that practically everything above the inferred structural floor disappeared.

And a raw 38% in a hyperpartisan era might conceivably normalize to 80, 90, whatever the eventual model says.

That's exactly the communication problem you originally identified. Someone hears:

38% approval

and intuitively sees a gauge that's still more than a third full.

Whereas:

Presidential Disenchantment Index: 91/100

would communicate:

Relative to historically movable presidential support, this is an extraordinarily severe collapse.

without pretending that the remaining 38% of people don't exist.

One refinement to the historical development period

I agree with starting around Eisenhower because Gallup's presidential polling becomes rich enough for longitudinal work. But I wouldn't throw Truman away. Gallup's presidential approval series actually begins with Truman in 1945, and his presidency contains an extraordinary 22–23% low depending upon the exact series/measurement convention.

That gives us a useful pre-Eisenhower boundary case.

So I'd probably structure the eventual analysis as:

Primary fitting period: Eisenhower (1953) through Obama (pre-2016).

Earlier validation data: Truman, where comparable measurements permit.

Floor case study: Nixon/Watergate examined especially closely rather than mechanically treated as another observation.

Held-out regime: 2016 onward.

That protects the cleaner dataset while giving us two historically fascinating extreme observations—Truman and Nixon—to see whether our inferred floor behaves sensibly.

And importantly, we shouldn't just use each president's minimum. We have longitudinal approval series. The trajectory toward the floor contains information.

If Nixon goes:

[ 60\rightarrow50\rightarrow40\rightarrow30\rightarrow24 ]

and different demographic/party groups peel away at different stages, that's vastly more informative for estimating (P), (R), and the persuadable component than the final 24 by itself.

The bottom tells us where he ended.

The collapse tells us what the 24 is made of.

That's probably the next analytical step before inventing more equations: establish the historical dataset and look specifically at election share, victory margin, approval trajectory, partisan approval trajectory where available, and major historical shocks, without yet fitting the normalization. We'd be examining the instrument while it was supposedly still working before deciding mathematically how to recalibrate it.

And I think your "broken instrument" formulation captures the larger project nicely: we aren't trying to modify the old approval scale until Trump looks unusual. We're trying to reconstruct what information the approval scale historically contained, and only afterward ask whether the same raw numbers still contain the same information. memcite

G: [Non-text content: thoughts; content_type=thoughts]

G: [Non-text content: reasoning_recap; content_type=reasoning_recap]

G: I agree with both modifications, and the historical record supports your instinct about time-in-office needing to be represented somehow rather than treating every decline from Election Day as disenchantment.

Gallup’s pre-2016 record shows a real honeymoon phenomenon, but not a fixed one. Among postwar presidents, the median time to first fall below 50% approval was about 13 months, while the average was 23 months; some presidents fell below 50% in their first year, while Eisenhower did not do so until year five. George W. Bush is also an obvious demonstration of why the function cannot simply be “approval naturally decays with time”: his approval was already nearing 50% before September 11, then jumped dramatically afterward. citeturn274664search1turn274664search3

So I would make an important distinction in the eventual prototype:

[ \text{Observed decline}= \text{normal honeymoon decay} + \text{event effects} + \text{disenchantment} ]

The first term there is what you're getting at. A president is normally inaugurated with something resembling a temporary presumption of goodwill. Some of that support is not really earned support that can subsequently be described as having become disillusioned. It's more like an introductory allowance.

The data make that fairly visible. Before Trump, first-year approval averages for elected presidents from Eisenhower through Obama ranged from Clinton's 49.3% on the low end to Kennedy's 76.4%; most were above 57%. Gallup explicitly describes this as the presidential honeymoon. citeturn274664search2

So I wouldn't want our index to say that, for example, somebody going from 65 shortly after inauguration to 58 six months later has necessarily accumulated seven points of disenchantment. Some fraction is just the honeymoon wearing off.

That suggests a small time function, provisionally something like:

[ H(t) ]

where (H) is the expected honeymoon premium remaining at month (t).

Then instead of comparing raw approval directly, we'd first estimate:

[ A^*(t)=A(t)-H(t) ]

where (A^*) is something like underlying approval after removing the expected early-term premium.

I would absolutely not assume (H(t)) is linear. The first prototype could deliberately make it embarrassingly simple—perhaps an exponential or piecewise decline over the first 12–18 months—and then see where it breaks. That's exactly consistent with the experimental philosophy you're specifying.

And I strongly agree with your treatment of (P).

It should be:

[ P_t ]

or, if we're working election-to-election,

[ P_e ]

not simply (P).

If Nixon's 24% turned out to be our best empirical observation of something close to the patriotic floor, the correct statement would be:

[ P_{1974}\approx24% ]

not:

[ P=24% ]

because the event that allows us to see the variable may itself change the variable.

That's an unusually important point here. Watergate may simultaneously provide the cleanest measurement of presidential deference and damage presidential deference. So the measurement resembles taking someone's blood pressure during the event that permanently altered their cardiovascular system. You learn something real, but you cannot blindly export the value backward and forward through time.

And I wouldn't even assume your proposed upper bound—that (P_t) probably never again exceeds 24%—inside the model. I think it's a plausible historical hypothesis, particularly given declining institutional trust and changes in media environment, but it would be more useful if the model were allowed to surprise us. There could conceivably be a later patriotic revival under some national circumstance.

Your pre-Eisenhower idea is methodologically cleaner

I agree. I would now divide the experiment into three regimes:

[ \boxed{\text{Pre-Eisenhower}} \quad|\quad \boxed{\text{Eisenhower–2015}} \quad|\quad \boxed{\text{2016 onward}} ]

The middle period is the construction set.

The earlier period becomes a backward extrapolation test.

The later period becomes a forward extrapolation/stress test.

That's actually better than mixing Truman into development, because it gives us two opportunities to test whether the equation captures something real.

If we develop a model entirely from 1953–2015 and then discover that it does a reasonably good job describing Truman despite never having seen Truman, that's evidence that we've captured some underlying political behavior rather than merely curve-fitting presidents.

Then we throw the same untouched equation at 2016 onward.

If it suddenly develops enormous systematic residuals, that's evidence of regime change.

And those two tests aren't equivalent. The first asks:

Does this instrument generalize into an earlier political/media environment?

The second asks:

Does it survive the transition into modern hyperpartisanship?

Very useful distinction.

I also like “homeostatic variable”

That is almost exactly how I would conceptualize (P_t).

Not a constant.

Not random noise.

A variable with inertia.

Something like:

[ P_{t+1}=P_t+\Delta P_t ]

where ordinarily:

[ |\Delta P_t|\ll1 ]

but major events can produce unusually large changes.

Watergate might produce a negative shock.

9/11 might temporarily produce a positive shock—not necessarily to the underlying long-term patriotic floor, though. That's something we'd need the model to distinguish.

I'd probably eventually separate:

[ P_t = P_t^{base}+S_t ]

where (P^{base}) is slow-moving institutional/patriotic deference and (S_t) is a temporary rally shock.

That would prevent 9/11 from making us conclude that the American population suddenly acquired a permanently enormous patriotic approval floor. George W. Bush reached 90% approval in September 2001; obviously that cannot be interpreted as a permanent structural change in the accessible scale, since he eventually reached 25%. citeturn274664search0

That high-to-low movement is actually going to be an extraordinarily useful stress case.

And I strongly agree with your instruction for the first prototype.

I would explicitly optimize Prototype 1 for falsifiability, not fit.

In other words, I don't want to produce some twelve-parameter equation that beautifully reproduces every president from Eisenhower through Obama. That tells us almost nothing, because with enough knobs we can make virtually anything fit.

I'd rather produce something with perhaps four or five meaningful inputs:

[ D=f(A,V,M,P_t,H(t)) ]

where initially:

• (A) = observed approval,
• (V) = election vote share,
• (M) = electoral margin,
• (P_t) = estimated patriotic floor at that historical point,
• (H(t)) = honeymoon adjustment.

And deliberately leave several things out.

Then we run every presidency from Eisenhower through Obama through it and ask:

Where does it give obviously stupid answers?

Those failures tell us what variable is missing.

If Reagan breaks it because recession/recovery produces a weird trajectory, that's information.

If George H.W. Bush breaks it because the Gulf War creates an enormous rally followed by collapse, that's information.

If Clinton breaks it because approval and electoral mandate behave strangely after impeachment, that's information.

If George W. Bush completely destroys the equation because 9/11 temporarily moves the accessible political range itself, that's extremely valuable information.

And Nixon is probably our best candidate for asking whether the inferred lower asymptote behaves sensibly.

So the first model's output shouldn't be treated as:

Here is the Presidential Disenchantment Index.

It should really be:

Here is PDI-0.1. Now let's attack it.

That fits your larger point perfectly. We're building a measuring instrument for something that isn't directly observable. The first useful accomplishment isn't getting the calibration right. It's discovering which physical forces our first instrument forgot existed. memcite

G: [Non-text content: reasoning_recap; content_type=reasoning_recap]

G: Nothing you just added disturbs the model. It actually gives version 0.1 a cleaner architecture, because the honeymoon and event effects can both be treated as temporary deviations from an underlying approval state rather than being confused with disenchantment itself.

I would make PDI-0.1 deliberately simple enough that we can see exactly why it fails.

The central idea would be:

[ \boxed{ D_t

100\left[ 1- \frac{A_t^{,*}-F_t} {B-F_t} \right] } ]

where (D_t) is the Presidential Disenchantment Index at time (t).

The terms need unpacking, because almost all of the real argument is hiding inside them.

1. Correct observed approval for temporary effects

Start with raw approval (A_t), but don't immediately call every movement disenchantment.

Define:

[ A_t^{,*}=A_t-H_t-S_t ]

where:

• (H_t) = ordinary first-term honeymoon premium;
• (S_t) = temporary event effect, which can be positive or negative.

So a patriotic rally might mean:

[ S_t>0 ]

while an anti-honeymoon caused by some catastrophic national condition might mean:

[ S_t<0 ]

This is useful because we don't need separate equations for "second honeymoon" and "anti-honeymoon." They can initially be the same event-response function with a signed amplitude.

Something crude but nonlinear would work for 0.1:

[ H_t=H_0e^{-kt} ]

with (k) chosen so that (H_t) is practically negligible by roughly 18–23 months.

I'd probably define "practically negligible" rather than mathematically zero. Exponentials never actually reach zero, which conveniently matches what we're saying anyway.

For example, if we want only 5% of the initial honeymoon effect remaining after 23 months:

[ e^{-23k}=0.05 ]

which gives approximately:

[ k\approx0.13 ]

So:

[ \boxed{H_t=H_0e^{-0.13t}} ]

with (t) measured in months.

I would not yet specify (H_0). That's something the historical data should estimate.

The event-response term can initially use the same shape:

[ \boxed{ S_t=s,e^{-\lambda(t-t_s)} } \qquad t\geq t_s ]

where:

• (t_s) = time of the event,
• (s) = signed size of the event response,
• (\lambda) = rate at which it dissipates.

Thus 9/11 might have an enormous positive (s); a severe national disaster could conceivably have negative (s).

If bin Laden's death produces a smaller, shorter rally:

[ s_{\text{UBL}}>0,\qquad \lambda_{\text{UBL}}>\lambda_{9/11} ]

Same mechanism, different magnitude and duration.

That is exactly the kind of simplification I want in 0.1.

2. Establish the president's election baseline

This is where our earlier distinction between absolute coalition size and electoral margin comes back.

Let:

[ V=\text{president's popular-vote share} ]

[ M=V-O ]

where (O) is the principal opponent's share.

For version 0.1, I would not immediately mash those into one mysterious weighted equation. That would conceal whether the absolute vote or the margin is doing useful work.

Instead define the initial support baseline as:

[ \boxed{B=V+\alpha M} ]

where (\alpha) is deliberately left as a coefficient to test.

This may look almost offensively simple, but that's useful.

If:

[ \alpha=0 ]

we are saying only coalition size matters.

If:

[ \alpha>0 ]

we're saying electoral dominance contains additional information beyond the winner's raw coalition.

If the historical data tell us (\alpha\approx0), your original concern about margin turns out not to improve the instrument.

If (\alpha) is substantial, we've learned something.

And if it behaves completely differently in landslides versus close elections, we'll know the linear (M) term is wrong and needs curvature.

For Trump 2024, just illustratively:

[ V\approx49.8,\qquad M\approx1.5 ]

so:

[ B=49.8+1.5\alpha ]

A tiny margin barely alters the baseline.

A 58–40 landslide gives:

[ B=58+18\alpha ]

and therefore explicitly recognizes that a landslide carried information not contained in 58 alone.

I suspect this term will eventually need combined major-party share as well, exactly for the third-party problem we identified. But I would leave that out of 0.1 on purpose and see which elections scream at us that it is missing.

3. Estimate the bottom of the traversable range

Instead of a universal (L), let's now call it:

[ \boxed{F_t} ]

for floor, because we already established that it changes historically.

And:

[ F_t=P_t+R_t ]

where:

• (P_t) = homeostatic patriotic/presidential floor;
• (R_t) = locked partisan support above that floor.

Crucially:

[ P_t\neq\text{constant} ]

and Nixon gives us, at most, something like:

[ P_{1974}\lesssim24 ]

or potentially:

[ P_{1974}\approx24 ]

if the evidence eventually supports your saturation hypothesis.

But I don't think version 0.1 should pretend we already know how to estimate (P_t) and (R_t) separately.

So for the first prototype I'd make an intentionally crude historical floor function:

[ \boxed{ F_t=P_t+\beta V } ]

where (\beta V) represents the fraction of the electoral coalition behaving as structurally locked support.

Again, (\beta) isn't an assertion. It's a coefficient we're trying to break.

This means:

[ D_t

100\left[ 1- \frac{A_t-H_t-S_t-(P_t+\beta V)} {(V+\alpha M)-(P_t+\beta V)} \right] ]

And therefore the complete ugly-but-useful PDI-0.1 is:

[ \boxed{ D_t

100 \left[ 1- \frac{ A_t

H_0e^{-0.13t}

S_t

P_t

\beta V }{ V+\alpha M-P_t-\beta V } \right] } ]

with:

[ S_t

\sum_i s_i e^{-\lambda_i(t-t_i)} ]

for any identified major temporary events.

That's my first actual prototype.

The interpretation remains extremely simple despite the machinery.

If:

[ D=0 ]

then after correcting for honeymoon/event effects, the president has retained essentially all of the contestable support associated with the election baseline.

If:

[ D=50 ]

roughly half of the traversable distance between the initial coalition state and the modeled structural floor has disappeared.

If:

[ D=100 ]

the president has reached the modeled floor:

[ A_t^*=F_t ]

And if:

[ D>100 ]

do not cap it.

That's an important testing choice.

A value of 117 is the equation telling us:

"The president has fallen below the floor you told me was supposed to exist."

That's exactly the kind of break we're looking for.

Likewise:

[ D<0 ]

means corrected approval has exceeded the election-derived baseline.

Don't cap that either.

A (-25) might be telling us about successful persuasion, an incorrectly modeled event rally, an incorrect election baseline, or some other missing mechanism.

For version 0.1, ugly outputs are diagnostics.

And I would explicitly define the places where we expect it to break

The first is Nixon. If our inferred (P_t+\beta V) leaves Nixon sitting comfortably above zero contestable support in August 1974, then either Nixon wasn't the saturation event we suspect or our floor model is wrong.

The second is George H.W. Bush. His enormous Gulf War approval spike should test whether the event term can distinguish temporary rally effects from genuine changes in contingent support.

The third is George W. Bush. He should torture virtually every component simultaneously: disputed/narrow election, pre-9/11 approval movement, gigantic 9/11 rally, prolonged wars, reelection, and eventual 25% approval. If PDI-0.1 survives him cleanly, I'd actually become suspicious that we've overfit it.

The fourth is Clinton, because his electoral vote share and approval relationship—especially with substantial third-party voting in 1992 and 1996—should expose the omission of major-candidate concentration.

The fifth is Reagan. His recession collapse followed by strong recovery tests something our current formulation barely contains: disenchantment may be reversible.

That's important.

Our equation allows it mathematically:

[ D_{t+1}<D_t ]

but our language has implicitly sounded like disenchantment accumulates monotonically.

It plainly doesn't have to.

Perhaps "disenchantment" is still a good name because people can become re-enchanted, but that will be something to watch conceptually.

There is one additional problem I deliberately would not solve yet: second terms.

The honeymoon function probably does not restart identically at reelection. A reelected president has neither the novelty nor uncertainty of a new president, but an election victory itself may create some temporary renewed mandate effect.

Instead of quietly assuming:

[ H_{\text{term 2}}=H_{\text{term 1}} ]

I'd initially set:

[ H_{\text{term 2}}=0 ]

and see whether second-term beginnings systematically break the model.

If they do, we add a reelection honeymoon coefficient later. That's more informative than guessing it into existence beforehand.

So PDI-0.1 has only a handful of things that eventually need empirical estimation:

[ H_0,\quad \alpha,\quad \beta,\quad P_t ]

plus event amplitudes and decay rates when major shocks occur.

And the core model is really just this conceptual diagram:

[ \boxed{ \text{Election baseline} \longrightarrow \text{remove temporary effects} \longrightarrow \text{measure distance toward structural floor} \longrightarrow 0\text{–}100\text{ disenchantment scale} } ]

I think this is primitive enough to be useful. I would resist adding anything else before actually throwing Eisenhower-through-Obama data at it. The omissions are now features: third-party vote, second-term honeymoon, economic conditions, approval measurement differences, partisan polarization drift, and possibly varying (P_t) are all waiting to reveal themselves by producing identifiable failures.

Version 0.1's job is therefore not to be right. Its job is to be wrong in ways that tell us what version 0.2 needs.

G: Yes — that is an important correction in framing, and I agree that it changes the purpose statement more than the mathematics.

This should be treated as a retrospective normalization model, not a predictive model.

Formally, the job is:

[ \boxed{ \text{historical raw approval data} ;\longrightarrow; \text{normalized approval/disenchantment measure} } ]

The equation is not trying to answer, “What will approval be next month?” It is trying to answer:

Given what we know about the electoral baseline, structural partisan support, patriotic floor, honeymoon effects, and exceptional events, what did a raw approval figure at time (t) actually mean relative to the politically movable range available at that time?

That distinction should govern how we build the next versions.

On (S), yes: in the formal definition, I would make it explicitly zero by default.

Something like:

[ S_t = 0 ]

unless an independently identified exceptional event is being modeled.

More formally:

[ S_t= \begin{cases} 0, & \text{if no exceptional event adjustment is specified}\ S_t^{(event)}, & \text{otherwise} \end{cases} ]

That keeps the base normalization clean. A researcher can't just introduce (S) because a data point looks inconvenient. The event has to be identified externally first.

And for the early versions I agree even more strongly with your refinement: we probably shouldn't actually calculate (S) at all.

Instead, flag observations such as September 2001 as:

[ S_t\neq0\quad\text{(suspected)} ]

and temporarily exclude or annotate them when fitting the ordinary normalization.

That's better methodology for 0.1 and probably 0.2. Otherwise the event function becomes an easy way of explaining away every failure.

The event adjustment should eventually be a corrective tool applied after the ordinary instrument works tolerably well.

The same principle applies to the honeymoon function, but with an important difference: honeymoon decay is ordinary enough that it belongs in the base instrument.

So for early versions I'd fix:

[ H_t=H_0e^{-kt} ]

with one common (H_0) and one common (k) estimated from the development period.

We deliberately accept that this is wrong at the individual-president level.

Later we could promote it to something like:

[ H_t=f(H_0,k,V,M,\ldots) ]

or:

[ H_{i,t}=H_{0,i}e^{-k_i t} ]

where the initial magnitude and decay constant vary by president.

And your example is exactly the sort of relationship we'd eventually test: perhaps a president entering with an enormous electoral mandate receives little additional honeymoon goodwill because much of it is already priced into the baseline; alternatively perhaps a landslide produces an even stronger honeymoon. We shouldn't decide which before seeing the residuals.

So (H) is initially generic correction, later potentially contextual correction.

Whereas (S) is initially annotation only, later potentially special-case correction.

That's a useful distinction.

I also agree about (\alpha).

When I wrote:

[ B=V+\alpha M ]

I called (\alpha) a coefficient because that's mathematically convenient, but conceptually we shouldn't become attached to the idea that:

[ \alpha=\text{one universal constant} ]

It is better to think of it initially as a placeholder for:

Whatever transformation tells us how much additional information electoral margin contributes beyond raw vote share.

Version 0.1 might use:

[ \alpha=\text{constant} ]

simply because that's the easiest thing to falsify.

But later:

[ \alpha=\alpha(V,M,C,\text{era},\ldots) ]

could emerge.

Or the entire expression (V+\alpha M) might disappear because we discover some more natural nonlinear construction.

So that's another place where the early equation is scaffolding rather than doctrine.

I would now slightly rename what we're constructing

"Presidential Disenchantment Index" is still a reasonable name for the output, because the direction from electoral/initial support toward the structural floor is intuitively disenchantment.

But the whole methodology should probably be called something like:

Presidential Approval Normalization Model

or

Historical Presidential Approval Normalization

with PDI as one derived scale.

That keeps us from accidentally treating "disenchantment" as a causal theory.

The model doesn't need to claim:

Voters became disenchanted because X occurred.

It merely says:

After adjusting the raw scale for historically non-responsive support and temporary systematic effects, this presidency occupied position (D) within its estimated traversable approval range.

That's analytical normalization.

Causality comes afterward.

That is also why I would revise one thing I said earlier. I described the model as separating:

[ \text{normal honeymoon decay} + \text{event effects} + \text{disenchantment} ]

That's a little too causal.

A safer formulation is:

[ \boxed{ A_t= F_t+ C_t+ H_t+ S_t } ]

where:

• (A_t) = observed approval,
• (F_t) = structurally resistant approval,
• (C_t) = contingent approval, the portion containing the substantive information we're trying to normalize,
• (H_t) = ordinary early-term distortion/premium,
• (S_t) = exceptional contextual deviation.

Then our normalization is fundamentally trying to recover and scale:

[ C_t ]

rather than claiming to explain why (C_t) changed.

That's much cleaner.

And the normalized disenchantment score is then derived from how much contingent support remains:

[ D_t

100\left(1-\frac{C_t}{C_0}\right) ]

where (C_0) represents the president's estimated contestable/contingent starting support.

That's arguably the conceptual heart of the entire project.

Everything else we're discussing is about estimating the numerator and denominator properly.

So I would rewrite PDI-0.1 conceptually as follows

First:

[ A_t^*=A_t-H_t ]

with (H_t) a generic exponential honeymoon adjustment.

For now:

[ S_t=0 ]

and known exceptional-event observations are flagged rather than corrected.

Then estimate a structural floor:

[ F_t=P_t+R_t ]

and an election-derived starting baseline:

[ B=g(V,M) ]

with, provisionally,

[ g(V,M)=V+\alpha M ]

Then the available contingent range at the start is:

[ C_0=B-F_t ]

and contingent support at observation (t) is:

[ C_t=A_t^*-F_t ]

therefore:

[ \boxed{ D_t

100\left( 1-\frac{A_t-H_t-F_t}{B-F_t} \right) } ]

That is simpler than the previous version, and I think it now reflects our actual intent better.

The still-unresolved pieces are:

[ B=g(V,M,\ldots) ]

[ F_t=f(P_t,R_t,\ldots) ]

[ H_t=H_0e^{-kt} ]

Those are normalization functions to estimate retrospectively, not forecasting parameters.

Then later, only after the base model behaves sensibly:

[ A_t^*=A_t-H_t-S_t ]

can replace the simpler adjustment for exceptional historical periods.

That gives us a much stricter rule:

Normal historical observations are used to build the instrument. Exceptional observations are initially used to test or flag the instrument, not to teach it how to excuse them.

I think that's a substantial methodological improvement over where I had drifted.

And your broader correction gets us back to the original reason for doing this: the problem isn't fundamentally that existing polls are "wrong." It's that the same raw numerical difference can contain radically different amounts of political information depending on how much of the nominal 0–100 range was realistically movable.

The normalization is an attempt to unflatten that information.

So 38% and 38% can remain perfectly valid poll results while the normalized interpretation might be:

[ 38_{\text{Era A}}\rightarrow D=65 ]

[ 38_{\text{Era B}}\rightarrow D=94 ]

because the underlying accessible ranges differed.

That's the instrument we're trying to build. memcite