# Questions tagged [voting-theory]

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### A ballot-casting problem

For any set $X$ and cardinal $\kappa$ let $[X]^\kappa$ denote the collection of subsets of $X$ with cardinality $\kappa$. If $n$ is a positive integer, let $[n]:=\{1,\ldots,n\}$. Let $V$ and $K$ be ...
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### 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 ...
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### 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 ...
304 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 ...
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### 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 ...