Michael Mandler

Incomplete preferences and rational intransitivity of choice

Do violations of classical rationality theory imply that agents are acting against their self-interest? To answer this question, we investigate whether completeness and transitivity necessarily hold when agents choose outcome rationally—that is, their choice sequences do not lead to dominated outcomes. We show that, because of the danger of money pumps and other manipulations, outcome rationality implies that agents must have transitive psychological preferences. Revealed preferences, on the other hand, must be complete since agents can be forced to choose from any set of options. But these justifications of transitivity and completeness cannot be combined. We show that if psychological preferences are incomplete then revealed preferences can be intransitive without exposing agents to manipulations or violating outcome rationality. We also show that a specific case of nonstandard behavior, status quo maintenance, is outcome-rational in the simple environments considered in the experimental literature, but not in more complex settings.

A Million Answers to Twenty Questions: Choosing by Checklist

Several decision models in marketing science and psychology assume that a consumer chooses by proceeding sequentially through a checklist of desirable properties. These models are contrasted to the utility maximization model of rationality in economics. We show on the contrary that the two approaches are nearly equivalent. Since the number of preference discriminations that an agent can make increases exponentially in the number of properties used, checklists provide a rapid procedural basis for utility maximization.

The Fragility of Information Aggregation in Large Elections

In a common-values election where voters receive a signal about which candidate is superior, suppose there is a small amount of uncertainty about the conditional likelihood of the signalʼs outcome, given the correct candidate. Once this uncertainty is resolved, the signal is i.i.d. across agents. Information can then fail to aggregate. The candidate less likely to be correct given agentsʼ signals can be elected with probability near 1 in a large electorate even if the distribution of signal likelihoods is arbitrarily near to a classical model where agents are certain that a particular likelihood obtains given that a specific candidate is correct.

Indifference and incompleteness distinguished by rational trade

We use an agents strict preferences to define indifference and incompleteness relations that identify the sequences of trades that are rational to undertake. If an agent makes sequences of trades of options labeled indifferent, the agent will never be led to an inferior outcome, but trades of options where no preference judgments obtain can lead to diminished welfare. For one-shot choices, in contrast, there can be no behavioral distinction between indifference and incompleteness. Applications include: an isomorphism for incomplete preferences that indicates when weak and strict preferences contain interchangeable information, a characterization of the (possibly incomplete) preference relations consistent with a one-shot choice function, and an equivalent definition of incompleteness that relies on the philosophical theory of incommensurability.

Classical and Neoclassical Indeterminacy in One-shot Versus Ongoing Equilibria

I analyze two connections between neoclassical and classical economics. First, I consider the indeterminacy that arises for both schools: In the neoclassical theories of overlapping generations and of factor pricing and in Sraffas price theory. Neoclassical indeterminacy occurs only in environments where relative prices can change through time; otherwise, determinacy obtains. Although these results challenge the Sraffian position on indeterminacy, the classical principle that current economic activity is embedded in the past proves to be a powerful insight: It establishes the robustness of factor-price indeterminacy and casts doubt on the importance of overlapping-generations indeterminacy. Second, I argue that recent claims that capital-theoretic paradoxes arise in intertemporal general equilibrium modes, not just in aggregative theory, cannot be validated.

Sraffian Indeterminacy in General Equilibrium

The indeterminacy claim for competitive price systems made by Sraffa (1960) is examined by placing Sraffas work in an intertemporal general equilibrium model. We show that indeterminacy occurs at a natural type of equilibrium. Moreover, the presence of linear activities instead of a differentiate technology is crucial and the indeterminacy is constructed, as in Sraffa, by fixing some or all of the economys aggregate quantities. On the other hand, an extra condition, that some factors have inelastic excess demand is necessary, and, unlike Sraffas model, relative prices must be allowed to vary through time. Sraffian indeterminacy and the generic finiteness of the number of equilibria are reconciled by showing that indeterminacy occurs at a measure-zero set of endowments. We use an overlapping-generations model to show that these endowments nevertheless arise systematically and that indeterminacy does not occur when relative prices are constant through time.

Rational agents are the quickest

Suppose an agent chooses by proceeding through a sequence of criteria: for any pair of alternatives the first criterion that ranks the pair determines the agents choice. Given any constraint on the capacity of the criteria to discriminate, choices that maximize complete and transitive preferences are always the outcome of a ‘quick’ sequence that uses the minimum number of criteria. For any irrational preference on the other hand there is always a discrimination constraint such that the preference is not the outcome of a quick sequence. When an agent uses attributes to form criteria and each attribute is rationally ordered, a quick sequence that leads to rational preferences necessarily arises.

Endogenous Indeterminacy and Volatility of Asset Prices Under Ambiguity

If agents are ambiguity-averse and can invest in productive assets, asset prices can robustly exhibit indeterminacy in the markets that open after the productive investment has been launched. For indeterminacy to occur, the aggregate supply of goods must appear in precise configurations but the investment levels that generate these supplies arise systematically. That indeterminacy arises only at a knife-edge set of aggregate supplies allows for a simple explanation of the volatility of asset prices: small changes in supplies necessarily lead to a big price response.

How to win a large election

We consider the optimization problem of a campaign trying to win an election when facing aggregate uncertainty, where agentsʼ voting probabilities are uncertain. Even a small amount of uncertainty will in a large electorate eliminate many of counterintuitive results that arise when voting probabilities are known. In particular, a campaign that can affect the voting probabilities of a fraction of the electorate should maximize the expected difference between its candidateʼs and the opposing candidateʼs share of the fractionʼs potential vote. When a campaign can target only finitely many voters, maximization of the same objective function remains optimal if a convergence condition is satisfied. When voting probabilities are certain, this convergence condition obtains only at knife-edge combinations of parameters, but when voting probabilities are uncertain the condition is necessarily satisfied.

Strategies as states

We define rationality and equilibrium when states specify agents’ actions and agents have arbitrary partitions over these states. Although some suggest that this natural modeling step leads to paradox, we show that Bayesian equilibrium is well defined and puzzles can be circumvented. The main problem arises when player j’s partition informs j of i’s move and i knows j’s strategy. Then i’s inference about j’s move will vary with i’s own move, and i may consequently play a dominated action. Plausible conditions on partitions rule out these scenarios. Equilibria exist under the same conditions, and more generally equilibria usually exist.