Homogeneity criterion

The Homogeneity criterion is a voting system property formulated by Douglas Woodall. The property is satisfied if, in any election, the result depends only on the proportion of ballots of each possible type. Specifically, if every ballot is replicated the same number of times, then the result should not change. Woodall considers Homogeneity to be one of several voting method properties "sufficiently basic to deserve to be called axioms."[1]

Complying methods

Any voting method that counts voter preferences proportionally satisfies Homogeneity, including voting methods such as Plurality voting, Two-round system, Single transferable vote, Instant Runoff Voting, Contingent vote, Coombs' method, Approval voting, Anti-plurality voting, Borda count, Range voting, Bucklin voting, Majority Judgment, Condorcet methods and others.

Noncomplying methods

A voting method that determines a winner by eliminating candidates not having a fixed number of votes, rather than a proportional or a percentage of votes, may not satisfy the Homogeneity criterion.

Example of Proportional Preference Profiles

The following four voter preference profiles show rankings of candidates by voters that are proportional.

Profile 1

# of voters Preferences
6 A > B > C
3 B > A > C
3 C > B > A

Profile 2

Ratio of voters Preferences
.5 A > B > C
.25 B > A > C
.25 C > B > A

Profile 3

Percent of voters Preferences
50% A > B > C
25% B > A > C
25% C > B > A

Profile 4

Fraction of voters Preferences
${\displaystyle {\tfrac {1}{2}}}$ A > B > C
${\displaystyle {\tfrac {1}{4}}}$ B > A > C
${\displaystyle {\tfrac {1}{4}}}$ C > B > A

A voting method satisfying Homogeneity will return the same election results for each of the four preference profiles.

References

1. ^ Woodall, Douglas, Properties of Preferential Election Rules, Voting matters - Issue 3, December 1994
• D R Woodall, "Properties of Preferential Election Rules", Voting matters, Issue 3, December 1994 [1]