Arrovian juntas

This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the classification of all such voting systems as dictatorial hierarchies. If we leave the traditional realm of complete orderings, the picture changes. Here we consider the more general setting where alternatives may be incomparable, that is, we allow orderings that are reflexive and transitive but not necessarily complete. Instead of a dictator we exhibit a junta whose internal hierarchy or coalition structure can be surprisingly rich. We give an explicit description of all such voting systems, generalizing and unifying various previous results.Comment: 22 pages, 1 figur

Arrovian juntas

This article explicitly constructs and classifies all arrovian voting systems on three or more alternatives. If we demand orderings to be complete, we have, of course, Arrow's classical dictator theorem, and a closer look reveals the classification of all such voting systems as dictatorial hierarchies. If we leave the traditional realm of complete orderings, the picture changes. Here we consider the more general setting where alternatives may be incomparable, that is, we allow orderings that are reflexive and transitive but not necessarily complete. Instead of a dictator we exhibit a junta whose internal hierarchy or coalition structure can be surprisingly rich. We give an explicit description of all such voting systems, generalizing and unifying various previous results.rank aggregation problem; Arrow's impossibility theorem; classification of arrovian voting systems; partial ordering; partially ordered set; poset; dictator; oligarchy; junta

Fully Proportional Representation as Resource Allocation: Approximability Results

We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems).Comment: 26 pages, 1 figur

Coalitional power indices applied to voting systems

We describe voting mechanisms to study voting systems. The classical power indices applied to simple games just consider parties, players or voters. Here, we also consider games with a priori unions, i.e., coalitions among parties, players or voters. We measure the power of each party, player or voter when there are coalitions among them. In particular, we study real situations of voting systems using extended Shapley–Shubik and Banzhaf indices, the so-called coalitional power indices. We also introduce a dynamic programming to compute them.Peer ReviewedPostprint (published version

Accuracy: The fundamental requirement for voting systems

There have been several attempts to develop a comprehensive account of the requirements for voting systems, particularly for public elections. Typically, these approaches identify a number of "high level" principals which are then refined either into more detailed statements or more formal constructs. Unfortunately, these approaches do not acknowledge the complexity and diversity of the contexts in which voting takes place. This paper takes a different approach by arguing that the only requirement for a voting system is that it is accurate. More detailed requirements can then be derived from this high level requirement for the particular context in which the system is implemented and deployed. A general, formal high level model for voting systems and their context is proposed. Several related definitions of accuracy for voting systems are then developed, illustrating how the term "accuracy" is in interpreted in different contexts. Finally, a context based requirement for voting system privacy is investigated as an example of deriving a subsidiary requirement from the high level requirement for accuracy

Applying Block Chain Technologies to Digital Voting Algorithms

Voting is a fundamental aspect to democracy. Many countries have advanced voting systems in place, but many of these systems have issues behind them such as not being anonymous or verifiable. Additionally, most voting systems currently have a central authority in charge of counting votes, which can be prone to corruption. We propose a voting system which mitigates many of these issues. Our voting system attempts to provide decentralization, pseudoanonymity, and verifiability. For our system, we have identified the requirements, implemented the backbone of the system, recognized some of its shortcomings, and proposed areas of future work on this voting system