Scarcity, Relative Payoffs and Political Irrationality

1. The empirical starting point: a society in which decline is credible

Saxony-Anhalt is not merely a convenient stage on which an ideological conflict happened to occur. It has structural characteristics that make a scarcity model politically plausible. At the end of 2025 its population stood at approximately 2.12 million, having fallen by 0.7 per cent in a single year. Official demographic projections envisage a decline of roughly 15 per cent between 2022 and 2040, while the working-age population is expected to contract even faster. Employment had already fallen again in the first quarter of 2026, continuing a negative trend that began in 2022. At the same time, 24.1 per cent of the population was classified in 2025 as being at risk of poverty or social exclusion, compared with 21.2 per cent nationally.

This does not mean that Saxony-Anhalt is literally running out of a fixed quantity of resources. Economies are not mechanically zero-sum. Productivity can increase, investment can create new resources, labour shortages may increase wages, fiscal transfers can redistribute resources across regions, and technological change can alter the production frontier.

What matters politically, however, is not merely the production frontier

but the frontier that voters believe they face,

Suppose that the objectively feasible aggregate resource pool at time $t$ is

where $T_t$ represents interregional or federal transfers. The relevant political quantity is instead

the individual's expectation of future resources conditional on the information set ${\mathcal{I}}_i$ that he actually processes.

The crucial psychological transition occurs when

for sufficiently many future periods. In ordinary language: I expect the future pie to be smaller than the present one. Once this expectation becomes persistent, political competition changes its structure.

2. From positive-sum politics to a perceived zero-sum game

Consider two social groups:

• $N$ = perceived native / in-group;
• $O$ = perceived outsider / out-group.

Let total distributable resources be $R$, divided between them:

If individuals believe that $R$ can expand, they may accept an allocation increasing both payoffs:

componentwise.

But suppose instead that

The psychologically salient constraint becomes approximately

The society has therefore moved from an objectively complex political economy into a subjectively zero-sum representation. This matters because the utility function itself can change.

The textbook individualistic utility function might be

Under scarcity and intergroup competition it may become

The parameter ${\rho }_i\ge 0$ measures the value assigned to one's relative position vis-à-vis the out-group. Then

If ${\rho }_i>0$, an improvement in the outsider's condition creates negative utility even though the individual's own material condition is unchanged. Conversely, $\Delta x_i<0$ does not necessarily imply $\Delta U_i<0$. A voter may accept losing five units if the disliked group loses twenty.

For example, let policy $M$ produce

and exclusionary policy $E$ produce

With $\rho =0.4$,

The individual loses five units of absolute welfare but gains five units of utility. This is not mathematically irrational. It is rational optimization of a preference that includes relative deprivation or out-group disutility. That distinction is uncomfortable but analytically indispensable. One cannot demonstrate irrationality merely by showing that a voter is prepared to hurt himself in order to hurt someone else more.

3. Why an outsider is strategically valuable as an enemy

An out-group has several characteristics that make it particularly efficient within this type of game. First, it is cognitively separable. Let the perceived social distance between individual $i$ and group $g$ be $d_{ig}$. We may define empathy or perceived commonality as

As social distance increases,

The psychological cost of imposing losses on the group consequently decreases. A more complete utility function can therefore be written as

where $L_O$ denotes harm imposed on the outsider and $\varphi$ the moral or empathetic cost of that harm. When

the third term largely disappears. The perfect political enemy is therefore not merely somebody who has fewer resources. It is somebody whose language, habits, religion, behaviour or cultural codes make him sufficiently alien that the voter is not required continually to simulate his point of view.

The outsider reduces a complicated distribution problem to a two-player game:

And a two-player game is cognitively far cheaper than a realistic model containing employers, asset owners, workers, pensioners, taxpayers, municipalities, federal transfers, demographic change, technological disruption, fiscal constraints and international capital flows. Political scapegoating is therefore not only emotional. It is also a form of dimensionality reduction.

The explanatory error can be enormous while the cognitive economy is considerable. A parallel mechanism — the compression of a high-dimensional social problem into a single legible political signal — is developed in The “Anti-Maranza” Bill.

4. Why promises of welfare retrenchment may cease to frighten voters

This is where the long-term rhetoric of mainstream government becomes strategically important. Suppose voters repeatedly hear, over several electoral cycles, statements equivalent to

where $W_t$ represents pensions, health provision, unemployment protection or public services.

The message may be justified in each individual case by demographic pressure, fiscal sustainability or economic reform. But repeated exposure changes expectations. If

then welfare contraction becomes incorporated into the baseline. The voter no longer compares full welfare against reduced welfare. He compares reduced welfare under party A with reduced welfare under party B.

Let the status-quo expectation be

although the previous historical reference point was

A mainstream party offers $W_M=68$. A radical challenger offers $W_R=60$.

Measured against the historical reference point:

But measured against the psychologically relevant baseline:

The apparent policy distance has shrunk by 75 per cent. And if the radical party additionally promises to reduce the outsider's access from $W_O=60$ to $W_O=20$, a sufficiently strong relative-payoff parameter can reverse the ranking.

The radical option is preferred whenever

A voter needs to assign only one quarter as much importance to relative advantage as to his own welfare for the exclusionary policy to dominate. The radical party's decisive promise is therefore not necessarily “You will receive more.” It can simply be “They will receive much less.” That promise is cheaper.

5. Welfare chauvinism as a change in the set of legitimate players

The relevant political move is thus more sophisticated than straightforward laissez-faire. AfD politics combines anti-state and market-oriented tendencies with what can be called welfare chauvinism: social protection is not necessarily rejected in principle but increasingly conditional on membership of the legitimate community.

In game-theoretic terms, the political question shifts from maximizing welfare in the abstract to maximizing the welfare of the in-group subject to an exclusion rule:

where $\mathcal{P}$ is the set of players considered fully entitled to participate in redistribution.

This is a change not merely in allocation but in the rules defining admissible players. That distinction is powerful because reductions in total welfare can coexist with increased political satisfaction.

Suppose $W_M=100$ and $W_R=82$. The radical option destroys 18 units of aggregate welfare.

Yet suppose the out-group's allocation changes from 20 to 4. The in-group receives 80 under $M$, but 78 under $R$.

Therefore $R\succ M$ whenever

A relatively modest preference for status domination is sufficient to make an aggregate-welfare-destroying policy individually attractive.

6. The myth of the Golden Age as a causal-inference error

Scarcity alone does not explain nostalgia. The next mechanism concerns causal inference.

Suppose an individual observes two time series: social homogeneity $H_t\downarrow$ and perceived prosperity $P_t\downarrow$. He therefore observes

A plausible but invalid inference follows:

That is: we were more prosperous because we were more homogeneous.

But the true causal structure may instead involve hidden variables:

$Z_t$ = {demography, industrial restructuring, productivity, globalization, capital allocation, reunification effects, …}.

Homogeneity and prosperity then move together without the former causing the latter. The voter nevertheless performs an informal Bayesian update.

Let $G$ be the hypothesis that social heterogeneity caused decline. Bayes' rule requires

But human political reasoning rarely computes the full denominator or compares sufficiently many alternative hypotheses. The practical process is closer to

with distorted parameters $\alpha$ and $\beta$.

When the prior $P(G)$ is already high because culturally salient narratives associate disorder with outsiders, even weak evidence can produce a large posterior. The myth of the Golden Age is therefore a counterfactual inference failure.

The individual remembers past homogeneity plus past security and compares it with present diversity plus present insecurity. What he cannot observe is the missing counterfactual: present homogeneity plus the present economic structure. Yet this unavailable state is precisely what would be required to establish causality.

7. The overconfidence problem: “Welfare is for other people”

A second distortion concerns self-assessed vulnerability. Let $p_i$ be the actual probability that voter $i$ will require substantial public support during some future period through unemployment, illness, disability, old age, childcare, housing support or other social insurance. Let ${\hat{p}}_i$ be the individual's subjective estimate.

Define the optimism error:

If $O_i>0$, the voter underprices social insurance.

Consider two systems. Under the more protective system $M$:

Under the more market-oriented system $R$:

If the true probability of a negative shock is $p=0.30$,

The protective system is materially superior. But suppose the voter believes $\hat{p}=0.10$.

The ranking reverses: $E(C_M)>E(C_R)$, but $\hat{E}(C_R)>\hat{E}(C_M)$. The voter is not choosing against what he believes to be his interests. He is choosing against his interests because he has misestimated the state probabilities. This distinction is the starting point for measuring political irrationality properly.

8. Why the standard rational-actor model is insufficient

The canonical rational-choice model assumes:

• a stable preference ordering;
• sufficiently accurate beliefs;
• Bayesian updating;
• correct understanding of available strategies;
• expected-utility maximization.

Calling a political choice rational merely because we can reverse-engineer a utility function under which it is optimal makes rationality almost tautological. For any observed action $a^{\ast }$, one can invent a utility function satisfying

The theory then explains everything and therefore almost nothing.

A more useful framework distinguishes three objects:

• $U_i$ — the actual preference function;
• ${\hat{U}}_i$ — the preference function the actor behaves as though he possesses;
• ${\hat{P}}_i$ — the subjective probability distribution over future states.

The observed choice is

The relevant benchmark is instead

where $P$ is the best available estimate of the actual state distribution. The divergence $a_i\ne a_i^{†}$ is where analytically meaningful irrationality begins.

9. Political irrationality should be decomposed, not declared

There is no single mathematically meaningful quantity called “irrationality”. Several different deviations must be separated.

9.1 Belief irrationality

Suppose the true state distribution is $P$ and the voter's perceived distribution is ${\hat{P}}_i$. A natural distance measure is the Kullback–Leibler divergence:

The larger $D_{KL}$, the greater the informational distortion.

Since KL divergence is asymmetric, a more convenient bounded measure is the Jensen–Shannon divergence:

Then

This can quantify, for instance, systematic underestimation of unemployment, illness or pension dependence.

9.2 Decision irrationality: regret

The simplest measure is counterfactual regret. Define:

If $R_i=0$, the actor chose an objectively optimal action given his own preferences. If $R_i>0$, there existed another strategy that would have given him higher expected utility.

A normalized measure is

This is far more useful than simply calling a voter irrational.

10. Rationality parameters and Quantal Response

People do not necessarily choose the highest-valued option deterministically. A standard approach is the logit Quantal Response model:

The parameter ${\lambda }_i$ measures behavioural responsiveness to payoff differences.

But a high ${\lambda }_i$ does not demonstrate genuine rationality. An individual can react extremely consistently to an entirely false payoff model. Suppose ${\hat{U}}_i(R)-{\hat{U}}_i(M)=10$ while $U_i(R)-U_i(M)=-10$. With large $\lambda$, the person will choose $R$ almost certainly. He is therefore highly instrumentally consistent and highly substantively mistaken at the same time. This is exactly why political science should avoid identifying predictability with rationality.

11. Three different rationalities

Instrumental rationality — $R_I$. Does the actor efficiently select the action that maximizes his perceived payoff?

Epistemic rationality — $R_E$. Are his beliefs approximately calibrated to reality?

Preference rationality — $R_P$. Are his preferences temporally stable, internally consistent and not generated by obvious framing effects?

A political actor may therefore have

He is excellent at maximizing the wrong model. That is arguably a more realistic description of much political behaviour than either “rational voter” or “irrational mob”.

12. Adding identity to the payoff function

Now consider identity. Define the voter's utility under policy $a$ as

where:

• $M_i(a)$ is absolute material payoff;
• $D_i(a)=M_i(a)-M_O(a)$ is relative advantage over the out-group;
• $I_i(a)$ is identity payoff;
• ${\rho }_i$ measures relative-status preference;
• ${\eta }_i$ measures identity salience.

Under rising scarcity $s$, it is plausible that

As absolute gains become harder to obtain, positional goods become more valuable. This is consistent with a simple economic intuition. Suppose absolute utility has diminishing marginal returns:

When expected future $x$ stagnates, political competition can increasingly migrate toward quantities whose supply is intrinsically relative: status, rank, belonging, cultural dominance, priority of access and recognition. These are often zero-sum by construction. Political entrepreneurs therefore possess an incentive to convert a difficult positive-sum production problem into an easier zero-sum status problem.

13. A computational experiment

Methodological warning. This simulation is not an econometric estimate of Saxony-Anhalt. It contains synthetic voters and parameters chosen solely to show how the mechanism behaves. The fact that one calibration produces a figure close to the actual AfD vote is not evidence that the model has “explained 43.8 per cent”.

We can illustrate the mechanism computationally.

Consider $N=200,000$ artificial voters. Each voter has a true probability of needing substantial social protection:

This produces

But individuals systematically underestimate their vulnerability:

After truncation to admissible probabilities, the simulated mean becomes approximately

Thus the population's true mean vulnerability is 29.4%, while perceived vulnerability is only 16.2%.

Relative-status sensitivity follows

Now introduce a normalized scarcity variable

The mainstream/protective policy $M$ gives:

The radical/retrenchment strategy $R$ gives:

The radical programme therefore looks attractive to someone expecting to remain in the successful state, but substantially worse to someone hit by a negative shock.

We also assume that retrenchment modestly raises exposure to risk:

The actual expected material payoffs are

The voter, however, evaluates them using ${\hat{p}}_i$:

The out-group payoff is set to

Consequently the relative payoff from choosing $R$ rather than $M$ becomes

Finally,

Choice follows a quantal-response rule:

The resulting simulation is:

Scarcity s	Simulated support for R	Mean actual material difference R−M	Actual difference among R supporters	R supporters materially worse off
0.00	29.3%	−5.55	−4.06	84.3%
0.25	34.0%	−6.19	−4.67	87.2%
0.50	38.9%	−6.87	−5.32	89.7%
0.75	43.9%	−7.58	−6.02	92.1%
1.00	49.0%	−8.33	−6.77	94.1%

The striking result is not the 43.9 per cent figure. Again, that number is mechanically calibration-dependent. The interesting result is the direction of movement.

The radical strategy becomes more electorally attractive precisely while becoming materially worse.

Why? Because three quantities move in opposite directions:

Absolute payoff deteriorates. Relative payoff improves. Identity payoff improves. Once voters overweight the latter two, political demand can move away from material self-interest.

14. Potential payoff versus effective payoff

This suggests another useful distinction. Let

be the material payoff that policy $a$ could yield under the actor's actual future state, and

be the payoff actually obtained after uncertainty resolves.

Before the election:

But the voter decides using

Therefore three numbers may coexist:

Political irrationality can arise from the distance

We may define the payoff perception error

For a choice between two policies, the more politically important measure is the error in the payoff difference:

The most severe case occurs when the error changes the sign:

This is a preference-reversal-by-misperception. The actor believes $R>M$ when in fact $R<M$.

15. The difference between being wrong and being irrational

Yet even this requires care. Being factually wrong is not automatically irrational. Suppose available information is noisy. A Bayesian decision-maker can make the wrong prediction while remaining perfectly rational given the information available at the time.

Therefore the relevant quantity is not simply

We need to ask whether beliefs are appropriately calibrated to available evidence. Let

be the posterior a perfectly Bayesian actor would form from information set $J_i$. Then epistemic distortion is better represented by

The individual is epistemically irrational to the extent that his beliefs diverge not from omniscience, but from what could reasonably have been inferred from the evidence available to him. Citizens cannot know macroeconomic futures. But they can systematically ignore evidence that contradicts identity, exaggerate vivid threats, infer causality from temporal coincidence, update more strongly on confirming information than on disconfirming information, and underestimate risks that imply personal vulnerability. Those processes are measurable.

16. Identity-protective belief updating

Suppose evidence $e$ contradicts a politically useful belief $B$. A Bayesian updates according to

An identity-protective reasoner may instead behave as though

For confirming evidence, ${\omega }_i^{+}>1$. For disconfirming evidence, $0<{\omega }_i^{-}<1$.

Then identical evidential strength generates asymmetric updating. This produces path dependence. Once a narrative such as outsiders $\to$ decline has become identity-compatible, contrary evidence has progressively less power to dislodge it.

17. Repeated games and the political equilibrium of permanent scarcity

The most important mechanism is dynamic. This is not a one-shot election.

Consider an infinitely repeated political game. At each time $t$:

• public services decline or are expected to decline;
• mainstream actors explain constraints;
• voters lower their expected welfare baseline;
• challenger parties promise exclusion;
• political salience shifts from production to distribution;
• relative-payoff preferences intensify.

Let expected welfare evolve as

Let out-group hostility evolve according to

Then

Persistent expected welfare decline mechanically increases the political value of relative advantage.

Now suppose mainstream parties respond to radical electoral success by adopting some of the challenger's scarcity framing:

where $V_R$ is the radical vote share. We obtain a feedback system:

Under appropriate parameter values this can generate multiple equilibria: a low-hostility equilibrium $({\rho }_L,V_L)$ and a high-hostility equilibrium $({\rho }_H,V_H)$. Once political competition crosses the basin separating the two, simply demonstrating that exclusionary policies are economically inefficient may no longer restore the previous equilibrium. The voters are playing a different game.

18. Why “they will cut your welfare too” can be politically ineffective

This also explains why a common argument against radical-right economic programmes may fail. The message is: they will cut your welfare. But suppose the voter already believes

Then learning

contains almost no new information. The difference is

The warning has little marginal informational value.

By contrast, suppose the challenger credibly signals

That difference remains large. The campaign therefore operates on the dimension where differentiation is still possible: not more versus less welfare, but who is entitled to the remaining welfare. The same logic of strategic issue selection — competing on the dimension where the opponent cannot follow — is examined in The Ceuta Signal.

19. The prisoner’s dilemma hidden inside exclusion

There is also a collective-action problem. Suppose every subgroup tries to protect its resources by excluding another subgroup.

Consider two groups, A and B. Both can choose $C$ = cooperate in universal provision or $E$ = seek exclusionary advantage.

A stylized payoff matrix might be:

	B: C	B: E
A: C	10, 10	4, 12
A: E	12, 4	6, 6

Exclusion $E$ is individually tempting. Against cooperation:

Against exclusion:

Thus $E$ dominates $C$, producing $(E,E)$ with payoff $(6,6)$. Yet $(C,C)$ would have yielded $(10,10)$.

Scarcity politics can therefore create a classic Prisoner's Dilemma. Every group seeks to preserve its position by narrowing solidarity. Collectively, the insurance pool shrinks. The eventual result can leave virtually everybody worse off. A structurally similar failure of binding coordination among nominally allied players is analysed in The Wide Coalition as an Adversarial Decision System.

20. A possible mathematical index of political irrationality

If we want a quantitative measure, I would avoid a single raw label and construct a multidimensional index.

Let

measure normalized belief distortion;

measure normalized counterfactual regret;

measure choice inconsistency across equivalent framings; and

measure temporal inconsistency.

Then define

Therefore

A value near zero denotes a decision-maker who:

• holds reasonably calibrated beliefs;
• incurs little counterfactual regret;
• responds consistently to equivalent choices;
• maintains relatively stable preferences over time.

A value closer to one denotes increasing divergence across those dimensions. This would be a far more defensible mathematical concept of political irrationality than simply assigning the label to political preferences we dislike.

21. One more variable: perceived irrationality

There is also a second-order problem. People evaluate the rationality of other groups. Let voter $i$'s estimate of group $g$'s irrationality be

Out-groups are often assigned

In other words: they are irrational; we are responding rationally to their irrationality.

This belief can itself justify exclusion. Suppose the expected cost of cooperating with group $g$ is

As the perceived irrationality of outsiders increases, cooperation becomes less attractive:

The perception that outsiders are culturally incomprehensible therefore does not merely create dislike. It alters the estimated payoff of social cooperation.

22. The deepest paradox: rationality inside an irrational game

Suppose a voter has constructed the following model:

• resources are permanently declining;
• outsiders compete directly for those resources;
• outsiders have caused part of the decline;
• mainstream parties will cut welfare anyway;
• the voter himself is unlikely to need much social protection;
• an exclusionary government will impose disproportionate losses on outsiders;
• greater cultural homogeneity will restore stability.

Given those premises, voting for an exclusionary party may be entirely consistent.

The problem is that several premises may be badly wrong.

Thus $a_R$ can be a perfectly rational solution to ${\hat{G}}_i$, the voter's subjective game, while being a poor solution to $G$, the actual game.

That is the distinction conventional rational-choice language often misses. The question should therefore not be: “Why do irrational people vote against their interests?” Nor should it be: “Since they voted voluntarily, their choice must reveal their true interests and is therefore rational.” Both statements are analytically lazy.

The relevant question is:

How different is the game the voter believes he is playing from the game he is actually playing?

Conclusion: when politics stops promising that you will win

The result in Saxony-Anhalt is particularly significant because it occurred in a territory where demographic decline, social insecurity and economic vulnerability are not imaginary phenomena. The region lost population again in 2025, employment was falling in early 2026, and demographic projections imply a substantially smaller future labour force.

But objective insecurity does not mechanically produce any particular political response. Between economic conditions and voting lies a game constructed inside the voter's head.

When people expect collective resources to expand, politics can promise:

When they no longer believe that promise, political entrepreneurs can offer something else:

You may not become richer. You may not become safer. You may receive fewer public services. Your pension may be less secure. Your labour-market risk may increase. But perhaps someone whom you regard as alien will lose more than you do.

The relevant utility therefore becomes not

but

Once that happens, a society can enter the strange equilibrium in which citizens knowingly or unknowingly exchange absolute welfare for relative superiority.

And prolonged welfare retrenchment by mainstream governments can unintentionally prepare this equilibrium. If every established actor has spent decades communicating

the radical challenger no longer needs to persuade voters that sacrifice is necessary. The sacrifice has already been normalized. The challenger need only answer the remaining question: who should sacrifice first?

The immigrant, the culturally unfamiliar person, the alleged free rider and the social outsider are strategically ideal answers because they transform a complicated distributional conflict into a simple coordination game around membership.

The final mistake would be to call all of this “rational”. It would be equally mistaken to call it simply “irrational”. A person may be rational in selecting the best move in a model built from irrational probabilities, false causal relations, overconfidence, distorted counterfactuals and identity-protective preferences.

The mathematical object we need to study is therefore not rationality itself, but the distance

between the actual game and the perceived game. As that distance grows, perfectly coherent choices inside the subjective game can generate increasingly destructive outcomes in the real one.

That may be the most useful way to interpret the politics of scarcity.

When people cease to believe that politics can make them better off, the cheapest remaining political promise is no longer:

YOU WILL WIN.

It is:

SOMEONE YOU DISLIKE WILL LOSE MORE THAN YOU.

And, from the point of view of game theory, that is not the disappearance of strategic behaviour. It is the emergence of a different game.

References and empirical sources

Landeswahlleiter Sachsen-Anhalt. Official results of the 2026 state election in Saxony-Anhalt. https://wahlergebnisse.sachsen-anhalt.de/wahlen/lt26/erg_land.html

Statistisches Landesamt Sachsen-Anhalt. Population of Saxony-Anhalt at 31 December 2025 and demographic trends. https://statistik.sachsen-anhalt.de/news/news-details/212-mio-menschen-lebten-am-31122025-in-sachsen-anhalt

Statistisches Landesamt Sachsen-Anhalt. Employment in Saxony-Anhalt in the first quarter of 2026. https://statistik.sachsen-anhalt.de/news/news-details/erwerbstaetigkeit-in-sachsen-anhalt-im-1-quartal-2026-weiter-gesunken

Statistisches Landesamt Sachsen-Anhalt. Risk of poverty or social exclusion, 2025. https://statistik.sachsen-anhalt.de/fileadmin/Bibliothek/Landesaemter/StaLa/startseite/Daten_und_Veroeffentlichungen/Veroeffentlichungen/Statistische_Monatshefte/2026/6Z003_05_2026-A.pdf

Reuters. Reporting on AfD policy proposals in Saxony-Anhalt and Germany's reform debate, September 2026. https://www.reuters.com/