Social Choice Theory
Social choice theory addresses the methods and processes of collective decision making. Applications range from preference aggregation in small committees, voting in democratic elections at the regional and national level to questions of fair resolution of conflicting interests. Important properties of aggregation methods are, for instance, anonymity, unanimity, efficiency, monotonicity and strategy-proofness (incentive compatibility). Our research is devoted to the identification and design of aggregation methods that combine such properties.
The Condorcet paradox shows that pairwise majority voting may produce cyclic outcomes on an unrestricted preference domain. For instance consider three voters with their preferences:
Voter 1: a > b > c Voter 2: b > c > a Voter 3: c > a > b
A majority of voters prefers a to b, a majority prefers b to c, and a majority prefers c to a. This leads to the Condorcet cycle
a > b > c > a.
The absence of majority cycles can only be guaranteed under suitable domain restrictions, such that single-peaked preferences, preferences with ‘value-restrictions' or single-crossing preferences – these are so called Condorcet domains. Puppe and Slinko (2015) prove that all (closed) Condorcet domains satisfy a so called intermediateness condition with respect to an appropriate median graph. This property allows us to investigate the Condorcet domains in more detail.
The following figures depict graphical representations of those domains:
Experimental Voting Theory
We empirically test different voting rules in the allocation of public projects in a laboratory experiment. The mean rule is highly manipulable theoretically and we find indeed that subjects have a strong tendency to play the corresponding Nash equilibrium strategy. In contrast, median-based rules are more difficult to manipulate, and sometimes truth-telling is a weakly dominant strategy. While most subjects play a best response to truth-telling of all other voters, a significant fraction of them does not vote truthfully themselves.
Strategy-proofness requires that truth-telling is a (weakly) dominant strategy for all individuals in a collective decision making process. We introduce the concept of robust strategy-proofness on a domain which imposes a stronger requirement for the preferences all other agents have. While in general a strictly stronger requirement, our main result shows that for all tops-only social choice functions strategy-proofness and robust strategy-proofness on minimally rich domains are equivalent.
Judgement Aggregation addresses the formation of collective judgements on logically interconnected propositions. The famous doctrinal paradox shows that – just as in voting theory – inconsistencies can easily arise if the aggregation is done by simple issue-wise majority vote:
Single Peaked Preferences
It is proved that, among all restricted preference domains that guarantee consistency (i.e. transitivity) of pairwise majority voting, the single-peaked domain is the only minimally rich and connected domain that contains two completely reversed strict preference orders. It is argued that this result explains the predominant role of single-peakedness as a domain restriction in models of political economy and elsewhere. The main result has a number of corollaries, among them a dual characterization of the single-dipped domain; it also implies that a single-crossing (‘order-restricted’) domain can be minimally rich only if it is a subdomain of a single-peaked domain. The main conclusions are robust as they apply both to strict and weak preference orders.
Economic experiments enable the development and testing of new theories that aim at explaining agents’ economic behavior. By using controlled conditions, both in the lab and in the field, deviations from classical assumption in subjects’ behavior can be documented and classified. The importance of such experimental research has grown steadily during the last decades.