Honesty criterion

Honesty criterion

 * Step: indicates a generic passage of the counting (such as sum of the points, normalization of the vote, etc).
 * Update Step: indicates a passage in the count in which the form of one or more votes is changed.
 * Honesty Step: is an Update Step that makes a tactical vote equal to the respective honest vote, and this equality is also maintained in all subsequent counting Steps.

Definition
Given an honest vote and the respective tactical vote, different from each other, a voting system satisfies the Honesty criterion when, during the count, it's valid that: - there is always a Honesty Step, and there is the possibility that the Honesty Step isn't the last Update Step of the count. - in the Update Steps the tactical vote reduces or keep the deviation from the respective honest vote (it's weak, if this point isn't satisfied).

The verification consists of applying the changes made on the tactical vote, during Update Step, also to the honest vote and then comparing how much they differ from each other.

To satisfy this criterion it's necessary to make assumptions about the form of the tactical vote obtained from the honest one.

Even if the criterion is met, it's still necessary to evaluate how much is the deviation from the honest vote before and after the Update Step and how much it affects the result.

Perfect Honesty criterion
A voting system satisfies the Perfect Honesty criterion when the first Update Step of the count is the Honesty Step.

Positive effects
- It reduces the negative effects of tactical votes, that are hypothesized by the voting system, when this criterion is satisfied.

- It can drastically reduce the negative effects of IIA failure.

Not meet criterion
All systems that don't modify the vote in any way, cannot satisfy the Honesty criterion. If a voter uses a tactical vote in such systems, it will remain tactical until the end of the count. Some of these systems are:


 * First-Past-The-Post
 * Borda
 * Approval Voting
 * Score Voting

Other systems that don't meet this criterion:


 * IRV (there isn't always a Honesty Step)

Honesty Step only in end

 * STAR and similar with "automatic runoff" (before the runoff, which is the Honesty Step, the votes are totally tactical, and therefore manage to damage the result anyway).

Meet criterion
Some systems that meet Honesty criterion, under certain assumptions, are:


 * IRNR (like Distributed Voting)
 * Distributed Voting
 * Distributed Multi-Voting (closest to the Perfect Honesty criterion).