Construction of aggregation operators with noble reinforcement

This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements. <br /

Set-Monotonicity Implies Kelly-Strategyproofness

This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred to all elements of the latter. It is shown that set-monotonicity---a new variant of Maskin-monotonicity---implies Kelly-strategyproofness in comprehensive subdomains of the linear domain. Interestingly, there are a handful of appealing Condorcet extensions---such as the top cycle, the minimal covering set, and the bipartisan set---that satisfy set-monotonicity even in the unrestricted linear domain, thereby answering questions raised independently by Barber\`a (1977) and Kelly (1977).Comment: 14 page

On aggregation operators of transitive similarity and dissimilarity relations

Similarity and dissimilarity are widely used concepts. One of the most studied matters is their combination or aggregation. However, transitivity property is often ignored when aggregating despite being a highly important property, studied by many authors but from different points of view. We collect here some results in preserving transitivity when aggregating, intending to clarify the relationship between aggregation and transitivity and making it useful to design aggregation operators that keep transitivity property. Some examples of the utility of the results are also shown.Peer ReviewedPostprint (published version

The aggregate weak axiom in a financial economy through dominant substitution effects

Consider a two period financial economy with incomplete markets and with agents having von Neumann-Morgenstern utility functions. It is well known that when the economys endowments are collinear, the excess demand function will obey the weak axiom when certain mild restrictions are imposed on agents coefficient of relative risk aversion. This result is obtained through the application of a theorem on the law of demand (for individual demand) formulated independently by Milleron (1974) and Mitjuschin and Polterovich (1978). In this paper, we develop their arguments further and apply them to economies without collinear endowments. We identify conditions which guarantee that the economys excess demand function obeys the weak axiom near an equilibrium price.

Judgment aggregation in search for the truth

We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of ‘yes’ votes exceeds a particular quota

Delay in Strategic Information Aggregation

We study a model of collective decision making in which agents vote on the decision repeatedly until they agree, with the agents receiving no exogenous new information between two voting rounds but incurring a delay cost. Although preference conflict between the agents makes information aggregation impossible in a single round of voting, in the equilibrium of the repeated voting game agents are increasingly more willing to vote their private information after each disagreement. Information is efficiently aggregated within a finite number of rounds. As delay becomes less costly, agents are less willing to vote their private information, and efficient information aggregation takes longer. Even as the delay cost converges to zero, agents are strictly better off in the repeated voting game than in any single round game for moderate degrees of initial conflict.repeated voting; gradual concessions; small delay cost

On the convergence of iterative voting: how restrictive should restricted dynamics be?

We study convergence properties of iterative voting procedures. Such procedures are defined by a voting rule and a (restricted) iterative process, where at each step one agent can modify his vote towards a better outcome for himself. It is already known that if the iteration dynamics (the manner in which voters are allowed to modify their votes) are unrestricted, then the voting process may not converge. For most common voting rules this may be observed even under the best response dynamics limitation. It is therefore important to investigate whether and which natural restrictions on the dynamics of iterative voting procedures can guarantee convergence. To this end, we provide two general conditions on the dynamics based on iterative myopic improvements, each of which is sufficient for convergence. We then identify several classes of voting rules (including Positional Scoring Rules, Maximin, Copeland and Bucklin), along with their corresponding iterative processes, for which at least one of these conditions hold