Parikh and Wittgenstein

A survey of Parikh’s philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing’s famous paper, “On computable numbers, with an application to the Entscheidungsproblem” (Turing in Proc Lond Math Soc 2(42): 230–265, 1936/1937) and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh’s contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein’s so-called metaphilosophy (e.g., Horwich in Wittgenstein’s metaphilosophy. Oxford University Press, Oxford, 2012) as a kind of “dead end” quietism. From early work on the idea of a feasibility in arithmetic (Parikh in J Symb Log 36(3):494–508, 1971) and vagueness (Parikh in Logic, language and method. Reidel, Boston, pp 241–261, 1983) to his more recent program in social software (Parikh in Advances in modal logic, vol 2. CSLI Publications, Stanford, pp 381–400, 2001a), Parikh’s work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues

Comparative Politics of Strategic Voting: A Hierarchy of Electoral Systems

What is the impact of electoral rules on the way people make decisions in the voting booth? Traditionally the literature about electoral systems argues that the size of the district magnitude determines the amount of strategic voting. I argue, however, that different electoral systems provide incentives that potentially undermine or facilitate the Duvergerian logic in practice. Contrary to the literature the results indicate that the impact of the district magnitude on the frequency of strategic voting in a given polity is conditional on the type of seat allocation system that defines how votes get translated into parliamentary seats.

A Local-Dominance Theory of Voting Equilibria

It is well known that no reasonable voting rule is strategyproof. Moreover, the common Plurality rule is particularly prone to strategic behavior of the voters and empirical studies show that people often vote strategically in practice. Multiple game-theoretic models have been proposed to better understand and predict such behavior and the outcomes it induces. However, these models often make unrealistic assumptions regarding voters' behavior and the information on which they base their vote. We suggest a new model for strategic voting that takes into account voters' bounded rationality, as well as their limited access to reliable information. We introduce a simple behavioral heuristic based on \emph{local dominance}, where each voter considers a set of possible world states without assigning probabilities to them. This set is constructed based on prospective candidates' scores (e.g., available from an inaccurate poll). In a \emph{voting equilibrium}, all voters vote for candidates not dominated within the set of possible states. We prove that these voting equilibria exist in the Plurality rule for a broad class of local dominance relations (that is, different ways to decide which states are possible). Furthermore, we show that in an iterative setting where voters may repeatedly change their vote, local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state. Weaker convergence guarantees in more general settings are also provided. Using extensive simulations of strategic voting on generated and real preference profiles, we show that convergence is fast and robust, that emerging equilibria are consistent across various starting conditions, and that they replicate widely known patterns of human voting behavior such as Duverger's law. Further, strategic voting generally improves the quality of the winner compared to truthful voting

The Logic of Joint Ability in Two-Player Tacit Games

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality

"Approval Voting" lacks a sound moral base for the individual voter's choice of approval versus non-approval, especially when the Status Quo is neglected

"Approval Voting" is the voting mechanism reportedly used since 1987 by professional and scientific societies such as the Econometric Society, INFORMS, ASA, AMS, MAA, IEEE and the Social Choice and Welfare Society. The method lacks a sound moral base for the choice by individual members between approval and non-approval, especially when the Status Quo is neglected. Minority rights are better protected when every voter respects the uniform Status Quo, rather than allowing that every voter determines a private (secret) reference point. A better method than Approval Voting is the (Pareto-) Borda Fixed Point rule introduced in the literature in 2001.

The Parliament of the Experts

In the administrative state, how should expert opinions be aggregated and used? If a panel of experts is unanimous on a question of fact, causation, or prediction, can an administrative agency rationally disagree, and on what grounds? If experts are split into a majority view and a minority view, must the agency follow the majority? Should reviewing courts limit agency discretion to select among the conflicting views of experts, or to depart from expert consensus? I argue that voting by expert panels is likely, on average, to be epistemically superior to the substantive judgment of agency heads, in determining questions of fact, causation, or prediction. Nose counting of expert panels should generally be an acceptable basis for decision under the arbitrary and capricious or substantial evidence tests. Moreover, agencies should be obliged to follow the (super)majority view of an expert panel, even if the agency\u27s own judgment is to the contrary, unless the agency can give an epistemically valid second-order reason for rejecting the panel majority\u27s view

Strategic Voting in Multiparty Systems: A Group Experiment

The paper tests the theory of strategic voting for multiparty systems with proportional representation and coalition governments at the micro-level. The study focuses in particular on the question whether participation in repeated elections allows voters to learn from experience and enables them to optimize their decision behavior. An economic group experiment with decision scenarios of varying degrees of difficulty was used to test decision making at both the individual and group level. The results suggest that a majority of voters were able to pursue successful decision strategies and that the difficulty of the decision scenarios affected the voting performance of the participants as expected. However, a learning effect is not supported by the data.

Coordination, focal points and voting in strategic situations : a natural experiment

This paper studies coordination in a multi-stage elimination tournament with large monetary incentives and a diversified subject pool drawn from the adult British population. In the tournament, members of an ad hoc team earn money by answering general knowledge questions and then eliminate one contestant by plurality voting without prior communication. We find that in the early rounds of the tournament, contestants use a focal principle and coordinate on one of the multiple Nash equilibria in pure strategies by eliminating the weakest member of the team. However, in the later rounds, contestants switch to playing a mixed strategy Nash equilibrium

Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply. To this end, we present a framework that allows "shades of gray" of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.Comment: This is the full version of paper #6080 accepted to AAAI'1