Questions tagged [voting-theory]

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6 votes
0 answers
213 views

Recursive runoff voting schemes

Background: I will below describe a generalization of the following voting systems (what is meant by “voting system” will be defined formally below) which are occasionally used in the real world: “...
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1 vote
0 answers
38 views

rank-choice shared-resource fair-division

I'm looking for an algorithm or a paper that solves a problem with a particular set of properties. Imagine you have some number of rooms and some greater number of people. Each person should be ...
38 votes
8 answers
3k views

Is there a truly general voting impossibility theorem that applies to real elections?

The purpose of most political elections is to select from the set of candidates a predetermined number $n$ of successful candidates. (Often $n = 1$.) In brief, my question is: Has it been proved ...
  • 25.8k
5 votes
4 answers
320 views

Majority vote of total orders

Fix an odd natural number $k$. Suppose we have $k$ total orders on the same (finite) set $X$. Define a tournament on the vertex set $X$ by putting a directed edge $x\rightarrow y$ if a majority of ...
  • 4,557
4 votes
2 answers
9k views

Seeking a solution algorithm to the 3-partition problem

I need to divide 48 pieces of jewelry between 3 inheritors so as to give equal, or nearly equal value, to each. I have learned that this is called the 3-partition problem. I solved it for 9 pieces of ...
2 votes
0 answers
191 views

Forcing the existence of a Condorcet Winner

Suppose that there is an election with three candidate and an infinite number of voters whose opinion lie in a two-dimensional issue space according to some distribution, and that voter's candidate ...
18 votes
4 answers
811 views

Arrow's theorem and the postseason

There are a number of instances of sports teams intentionally losing matches in order to secure a more favorable situation in a playoff round. While this doesn't happen terribly often, when it does it'...