Characterising scoring rules by their solution in iteratively undominated strategies

We characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

Ordinal Theories and the Social Choice Analogy

We introduce and discuss the problems of intertheoretic incomparability and merely ordinal theories. We then introduce the analogy between decision-making under moral uncertainty and social choice, and explain how this analogy can help us to overcome these problems. The rest of the chapter is spent fleshing out how this idea can help us to develop a theory of decision-making under moral uncertainty that is applicable even when all theories under consideration are merely ordinal, and even when there is neither level-nor unit- comparability between those theories. We consider whether My Favourite Theory or My Favourite Option might be the right theory of decision-making under moral uncertainty in conditions of merely ordinal theories and incomparability, but reject both of these accounts. We defend the idea that, when maximizing choice worthiness is not possible, one should use the Borda Rule instead.

Interval-Scale Theories and Variance Voting

This chapter discusses how to take into account moral uncertainty over interval-scale measurable but non-comparable theories. Once again, we make use of the analogy between decision-making under moral uncertainty and voting. We give examples of interval-scale theories where it’s plausible to think that these theories are incomparable with each other and discuss what to do in such cases. Arguing against the Borda Rule and Ted Lockhart’s Principle of Equity Among Moral Theories, we argue in favour of an account we call variance voting. Finally, we discuss what to do in conditions where one has positive credence in some merely ordinal theories, some interval-scale but non-comparable theories, and some theories that are both interval-scale measurable and comparable with each other. We discuss whether the normalization used by this account should be done only within the decision-situation at hand, or whether it should be done over all possible decision-situations.

HESITANT FUZZY LINGUISTIC DNMA METHOD WITH CARDINAL CONSENSUS REACHING PROCESS FOR SHOPPING MALL LOCATION SELECTION

The hesitant fuzzy linguistic term set is an effective tool to express qualitative evaluations since it is close to human reasoning and expressing habits. In this paper, we propose a multi-expert multi-criterion decision-making method integrating the double normalization-based multi-aggregation (DNMA) method with a cardinal consensus reaching process, where the assessments of alternatives over multiple criteria are expressed as hesitant fuzzy linguistic term sets. To do so, the DNMA method involving double normalizations and three aggregation tools is extended to deal with the hesitant fuzzy linguistic information and derive the ranking of alternatives with respect to each expert. In addition, a cardinal consensus reaching process is introduced to help experts reach an acceptable consensus level. In other words, the soft consensus is considered in the multi-expert multi-criterion decision-making process. Subsequently, an extended Borda rule is developed to aggregate the subordinate ranks and integrated scores of alternatives, and then deduce the comprehensive ranking of alternatives. A case study is given to illustrate the practicability of the proposed method for selecting the optimal geographical location of a larger-scale shopping mall in the new urbanization for a construction investment agency. The proposed method is compared with other ranking methods to illustrate its advantages.