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5
votes
4answers
200 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
votes
2answers
3k 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
0answers
140 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 ...
16
votes
4answers
661 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 ...