Anonymous user
User:DCary/WIP/Beatpath: Difference between revisions
m
→Alternative formulation: Change emphasis for first use of Beat
imported>DCary (Fix links to examples pages) |
imported>DCary m (→Alternative formulation: Change emphasis for first use of Beat) |
||
| (One intermediate revision by the same user not shown) | |||
Line 3:
In an election, a '''beatpath''' is a sequence of candidates such that each candidate in the sequence beats the next one in a pair-wise contest.
Beatpaths can be used to describe the [[Condorcet paradox]], the [[Schulze method]], and the [[../Schwartz set |Schwartz set (draft)]] [[Schwartz set | (current)]].
Line 84:
===Alternative formulation===
Given the [http://en.wikipedia.org/wiki/Binary_relation binary relation]
:(X,Y) is in ''Beat'' if and only if candidate X pair-wise beats candidate Y
then the [http://en.wikipedia.org/wiki/Binary_relation#Operations_on_binary_relations transitive-reflexive closure] of ''Beat'' is a [http://en.wikipedia.org/wiki/Preorder preorder] on the set of candidates, and the [http://en.wikipedia.org/wiki/Preorder#Formal_definition natural partial order generated from that preorder] is the beatpath order defined above.
| |||