A voting system satisfies join-consistency (also called the reinforcement criterion) if combining two sets of votes, both electing A over B, always results in a combined electorate that ranks A over B.^[1] It is a stronger form of the participation criterion. Systems that fail the consistency criterion (such as instant-runoff voting or Condorcet methods) are susceptible to the multiple-district paradox, a pathological behavior where a candidate can win an election without carrying even a single precinct. Conversely, it can be seen as allowing for a particularly egregious kind of gerrymander: it is possible to draw boundaries in such a way that a candidate who wins the overall election fails to carry even a single electoral district.

Rules susceptible to the multiple-districts paradox include all Condorcet methods and instant-runoff (or ranked-choice) voting. Rules that are not susceptible to it include all positional voting rules (such as first-preference plurality and the Borda count) as well as score voting and approval voting.

There are three variants of join-consistency:

A voting system is winner-consistent if and only if it is a point-summing method; in other words, it must be a positional voting system or score voting (including approval voting).

As shown below for the Kemeny rule and majority judgment, these three variants do not always agree with each other (which contrasts with most other voting criteria). Kemeny is the only ranking-consistent Condorcet method, and no Condorcet method can be winner-consistent.

This example shows that Copeland's method violates the consistency criterion. Assume five candidates A, B, C, D and E with 27 voters with the following preferences:

Now, the set of all voters is divided into two groups at the bold line. The voters over the line are the first group of voters; the others are the second group of voters.

In the following the Copeland winner for the first group of voters is determined.