Consistency criterion
Encyclopedia
A voting system
is consistent if, when the electorate is divided arbitrarily into two (or more) parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative. Smith calls this property separability and Woodall calls it convexity.
It has been proven a preferential voting
system is consistent if and only if it is a positional voting system
. Borda count
is an example of this.
The failure of the consistency criterion can be seen as an example of Simpson's paradox
.
Voting system
A voting system or electoral system is a method by which voters make a choice between options, often in an election or on a policy referendum....
is consistent if, when the electorate is divided arbitrarily into two (or more) parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative. Smith calls this property separability and Woodall calls it convexity.
It has been proven a preferential voting
Preferential voting
Preferential voting is a type of ballot structure used in several electoral systems in which voters rank candidates in order of relative preference. For example, the voter may select their first choice as '1', their second preference a '2', and so on...
system is consistent if and only if it is a positional voting system
Positional voting system
A positional voting system is a ranked voting method in which the options receive points based on their position on each ballot, and the option with the most points wins....
. Borda count
Borda count
The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
is an example of this.
The failure of the consistency criterion can be seen as an example of Simpson's paradox
Simpson's paradox
In probability and statistics, Simpson's paradox is a paradox in which a correlation present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and it occurs when frequencydata are hastily given causal...
.