Aggregation of Votes with Multiple Positions on Each Issue

We consider the problem of aggregating votes cast by a society on a fixed set of issues, where each member of the society may vote for one of several positions on each issue, but the combination of votes on the various issues is restricted to a set of feasible voting patterns. We require the aggregation to be supportive, i.e. for every issue $j$ the corresponding component $f_j$ of every aggregator on every issue should satisfy $f_j(x_1, ,\ldots, x_n) \in \{x_1, ,\ldots, x_n\}$. We prove that, in such a set-up, non-dictatorial aggregation of votes in a society of some size is possible if and only if either non-dictatorial aggregation is possible in a society of only two members or a ternary aggregator exists that either on every issue $j$ is a majority operation, i.e. the corresponding component satisfies $f_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =x, \forall x,y$, or on every issue is a minority operation, i.e. the corresponding component satisfies $f_j(x,x,y) = f_j(x,y,x) = f_j(y,x,x) =y, \forall x,y.$ We then introduce a notion of uniformly non-dictatorial aggregator, which is defined to be an aggregator that on every issue, and when restricted to an arbitrary two-element subset of the votes for that issue, differs from all projection functions. We first give a characterization of sets of feasible voting patterns that admit a uniformly non-dictatorial aggregator. Then making use of Bulatov's dichotomy theorem for conservative constraint satisfaction problems, we connect social choice theory with combinatorial complexity by proving that if a set of feasible voting patterns $X$ has a uniformly non-dictatorial aggregator of some arity then the multi-sorted conservative constraint satisfaction problem on $X$, in the sense introduced by Bulatov and Jeavons, with each issue representing a sort, is tractable; otherwise it is NP-complete

Aggregation and Representation in the European Parliament Party Groups

While members of the European Parliament are elected in national constituencies, their votes are determined by the aggregation of MEPs in multinational party groups. The uncoordinated aggregation of national party programmes in multinational EP party groups challenges theories of representation based on national parties and parliaments. This article provides a theoretical means of understanding representation by linking the aggregation of dozens of national party programmes in different EP party groups to the aggregation of groups to produce the parliamentary majority needed to enact policies. Drawing on an original data source of national party programmes, the EU Profiler, the article shows that the EP majorities created by aggregating MEP votes in party groups are best explained by cartel theories. These give priority to strengthening the EP’s collective capacity to enact policies rather than voting in accord with the programmes they were nationally elected to represent

Count the Limbs: Designing Robust Aggregation Clauses in Sovereign Bonds

On August 29, 2014, the International Capital Market Association (ICMA) published new recommended terms for sovereign bond contracts governed by English law. One of the new terms would allow a super majority of creditors to approve a debtor’s restructuring proposal in one vote across multiple bond series. The vote could bind all bond holders, even if a series voted unanimously against restructuring, so long as enough holders in the other series voted for it. An apparently technical change, awkwardly named “single-limb aggregated collective action clauses (CACs)” promised to eliminate free-riders for the first time in the history of sovereign bond restructuring. It could also open up new possibilities for abuse. The markets might have rebelled. Instead, they yawned … and proceeded to adopt the new terms. We consider why such consequential contract change met with less resistance than its relatively modest predecessors, series-by-series and two-limb aggregated CACs. We focus on contract design, and the process by which it came about. Most of the essay is devoted to analyzing the key features of single-limb aggregated CACs and the considerations that shaped decisions about these features. We conclude with observations on contract reform in sovereign debt restructuring and the challenges ahead

Information Aggregation in Standing and Ad Hoc Committees

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On the Computational Complexity of Non-dictatorial Aggregation

We investigate when non-dictatorial aggregation is possible from an algorithmic perspective, where non-dictatorial aggregation means that the votes cast by the members of a society can be aggregated in such a way that the collective outcome is not simply the choices made by a single member of the society. We consider the setting in which the members of a society take a position on a fixed collection of issues, where for each issue several different alternatives are possible, but the combination of choices must belong to a given set $X$ of allowable voting patterns. Such a set $X$ is called a possibility domain if there is an aggregator that is non-dictatorial, operates separately on each issue, and returns values among those cast by the society on each issue. We design a polynomial-time algorithm that decides, given a set $X$ of voting patterns, whether or not $X$ is a possibility domain. Furthermore, if $X$ is a possibility domain, then the algorithm constructs in polynomial time such a non-dictatorial aggregator for $X$. We then show that the question of whether a Boolean domain $X$ is a possibility domain is in NLOGSPACE. We also design a polynomial-time algorithm that decides whether $X$ is a uniform possibility domain, that is, whether $X$ admits an aggregator that is non-dictatorial even when restricted to any two positions for each issue. As in the case of possibility domains, the algorithm also constructs in polynomial time a uniform non-dictatorial aggregator, if one exists. Then, we turn our attention to the case where $X$ is given implicitly, either as the set of assignments satisfying a propositional formula, or as a set of consistent evaluations of an sequence of propositional formulas. In both cases, we provide bounds to the complexity of deciding if $X$ is a (uniform) possibility domain.Comment: 21 page

Pork Barrel Politics in Postwar Italy, 1953-1994

This paper analyzes the political determinants of the distribution of infrastructure expenditures by the Italian government to the country’s 92 provinces between 1953 and 1994. Extending implications of theories of legislative behavior to the context of open-list proportional representation, we examine whether individually powerful legislators and ruling parties direct spending to core or marginal electoral districts, and whether opposition parties share resources via a norm of universalism. We show that when districts elect politically more powerful deputies from the governing parties, they receive more investments. We interpret this as indicating that legislators with political resources reward their core voters by investing in public works in their districts. The governing parties, by contrast, are not able to discipline their own members of parliament sufficiently to target the parties’ areas of core electoral strength. Finally, we find no evidence that a norm of universalism operates to steer resources to areas when the main opposition party gains more votes

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