Aggregation of Continuous Preferences in One Dimension

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. The complexity of manipulating realistic elections where the number of candidates is a small constant was recently studied [4], but the emphasis was on the question of whether or not a protocol becomes hard to manipulate for some constant number of candidates. That work, in many cases, left open the question: How many candidates are needed to make elections hard to manipulate? This is a crucial question when comparing the relative manipulability of different voting protocols. In this paper we answer that question for the voting protocols of the earlier study: plurality, Borda, STV, Copeland, maximin, regular cup, and randomized cup. We also answer that question for two voting protocols for which no results on the complexity of manipulation have been derived before: veto and plurality with runoff. It turns out that the voting protocols under study become hard to manipulate at 3 candidates, 4 candidates, 7 candidates, or never.

Trip destination and mode choice are highly influenced by travelers' perceptions and behaviors; selecting a destination and a vehicle for a trip are two interdependent problems. This paper presents and applies a disaggregate joint model for traveler destination and mode choice. The choice model uses fuzzy set and probability theory to deal with the uncertainty embedded in travelers' perceptions and behaviors. The model is structured as a decision tree in which the fuzzy and non-fuzzy classification of influential variables regarding destination selection and mode choice expand the tree. The most influential explanatory variables among all the variables categorized for travelers' household, trip, and living zone specifications are selected based on the maximizing information. An aggregation method is designed to provide aggregate estimates for transportation planning based on the suggested disaggregate choice model. A data-set of over 9000 home-based morning peak-hour trips in Shiraz, a large city in Iran, is used for model construction and evaluation. When compared with a multinomial logit (MNL) model, the suggested models' estimates are more accurate than the traditional MNL model.

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Politics. Please check back later for the full article.Narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called preference aggregation functions, social welfare functions, and social choice functions. But more broadly, social choice theory identifies, analyzes, and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield of the social sciences that examines what may be called “voting rules” of various sorts. While social choice theory typically assumes a finite set of alternatives over which voter preferences are unrestricted, the spatial model of social choice assumes that policy alternatives can be represented by points in a space of one or more dimensions, and that voters have preferences that are plausibly shaped by this spatial structure.Social choice theory has considerable relevance for the study of legislative (as well as electoral) institutions. The concepts and tools of social choice theory make possible formal descriptions of legislative institutions such as bicameralism, parliamentary voting procedures, effects of decision rules (e.g., supramajority vs. simple majority rule and executive veto rules), sincere vs. strategic voting by legislators, agenda control, and other parliamentary maneuvers. Spatial models of social choice further enrich this analysis and raise additional questions regarding policy stability and change. Spatial models are used increasingly to guide empirical research on legislative institutions and processes.

This contribution presents the results of an experimental investigation of the mechanical behaviour of granular materials with crushable grains under one-dimensional compression at medium to high stress. The material used for the experimental work is a Light Expanded Clay Aggregate (LECA) whose grains break at relatively low stress. Reconstituted samples were prepared with different initial grain size distributions and their evolution observed under one-dimensional compression. The grain size distributions before and after testing were used to calibrate a bimodal model obtained from the superposition of two Weibull functions. The observed evolution of the micro and macro diameters on loading are linked to the characteristics of the one-dimensional compressibility curve obtained under displacement controlled conditions, such as its shape and two characteristic stress values, namely the pre-consolidation stress and the stress corresponding to the point of inflection.

Arrow’s Impossibility Theorem is a classical result in social choice theory (a branch of economic theory), which states that any system of rules for combining (“aggregating”) individual preference relations into a single representative relation results in a “dictatorship” where the combined preference only reflects the wishes of a single individual (provided that the aggregation rule satisfies two basic criteria). Since the 1980s, this result has been reformulated and understood using algebraic topology. The topological approach offers some geometric intuition as to why Arrow’s theorem holds, and can also be used to find alternative hypotheses which may escape the dictatorship outcome. A thorough examination of such topological models constitutes the main body of this thesis. Recently, social choice theory has been generalized (resulting in a field called “judgment aggregation”), and results analogous to Arrow's theorem have been established. The second part of this thesis introduces this field of study, and studies how some of the techniques from topological social choice theory can be extended to understand dictatorship outcomes in the theory of judgment aggregation. Although the analysis is restricted to a rather simple case, it nonetheless highlights the potential for a more general topological model of judgment aggregation, and exposes the main challenges that must be overcome in constructing such a theory.

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox--which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation--including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow's theorem.

The Thurstone method is a method of aggregation of preferences that leads to ordering objects at an interval scale, in contrast to other methods of aggregation, the application of which results in obtaining the ordinal scale only. However, we demonstrate that the interval scale obtained by means of the Thurstone method is not fully reliable, as it is strongly susceptible to the problem of irrelevant alternatives, i.e., the order of two objects might be dependent on whether there is or not a third, completely independent object in the studied collectivity. The other issue examined in the paper is the formula that is to be minimised in the Thurstone method. Thurstone proposed a formula easy to be minimised with tabularised values of normal distribution. However, today’s calculation powers of computers make it possible to minimise another formula, which allows a better fit of observed frequencies to the predicted ones, and makes it possible to avoid the problem with empirical frequencies close to 1. The aim of the paper is to propose two improvements to the Thurstone method. The first one involves the application of the rule of thumb to the minimal spacing (in terms of standard deviations), below which the ordering of objects cannot be regarded as reliable, and the use of the method of empirical examining of the stability of order. The second of the proposed improvements consists in minimising a formula other than the original one, especially in the cases where empirical frequencies reach very high values.

Editorial: Introduction to Special Section on Evidence-Based Practices for Persons With Intellectual and Developmental Disabilities

There is growing interest in incorporating urban form indicators into transportation planning and travel analysis. These indicators typically are measured at a certain level of spatial aggregation (e.g., traffic analysis zone) and therefore are subject to the modifiable areal unit problem (MAUP) known primarily in the statistical and geographic literature but generally overlooked by transportation researchers. The presence of the MAUP can cause serious inconsistency in analytical results and consequently misinform policy making. This study diagnoses the MAUP in measuring urban form through empirical modeling of travel mode choice in the Boston, Massachusetts, region. Using data aggregated in grids with five cell sizes and at the transportation analysis zone, the census block group, and the block level, the study explores the sensitivity of coefficient estimates for population density, network pattern, and land use balance to data aggregation in predicting mode choice decisions. Having confirmed the presence of the MAUP, the study discusses three approaches for dealing with it. Using a grid with a cell size of 1/2 mi appears to be the most desirable method of data aggregation among the eight methods studied. The suggested improvements in methodology will help advance the inquiry on the link between urban form and travel.

The Swaps index (Apesteguia and Ballester, 2015) is a popular measure of rationality in the revealed preference literature. In this note, we show a connection between the Swaps index and the Kemeny rule, a well-known method of preference aggregation in social choice theory. Our new interpretation of the Swaps index makes it a suitable measure of menu dependence in preferences.

This paper proposes a distance-based aggregation and consensus method for preference-approvals with potential applications in group decision-making, recommendation systems, and social choice theory. Preference-approvals are a type of preference data where individuals provide a list of approved alternatives in addition to a strict ranking. The proposed method aims to synthesise individual preference-approvals into a unified consensus representing the group’s collective view. The consensus is the preference-approval, which minimises the average distance within the whole set of voters. The performance of the proposed method is investigated through a sensitivity analysis on the weighting parameter, two simulation studies, and two real-data applications.

Information retrieval on RDF data benefits greatly from additional provenance information attached to the individual pieces of information. Provenance information such as origin of data, certainty, and temporal information on RDF statements can be used to rank search results according to one of those dimensions. In this paper, we consider the problem of aggregating provenance information from different dimensions in order to obtain a joint ranking over all dimensions. We relate this to the problem of preference aggregation in social choice theory and translate different solutions for preference aggregation to the problem of aggregating provenance rankings. By exploiting the ranking orderings on the provenance dimensions, we characterize three different approaches for aggregating preferences, namely the lexicographical rule, the Borda rule and the plurality rule, in our framework of provenance aggregation.

A new approach for multiple attribute group decision making with interval-valued intuitionistic fuzzy information

Empirical Properties of Group Preference Aggregation Methods Employed in AHP: Theory and Evidence

Wind turbines type and number choice using combinatorial optimization