# Runoff voting

A voting system used in single-seat elections. This system is used widely throughout the world.

### Voting

In the preliminary election, voters selects their preferred candidate. If one candidate reaches the election threshold (usually fifty percent), they are declared elected. Otherwise, the top candidates (usually the top two) are placed on a secondary ballot. Whoever receives the most votes on the second ballot is declared elected.

### An Example

30 voters. 50% threshold. Maximum of two candidates in the second round.

First ballot:

No candidates have achieved the threshold, so a second ballot is necessary. The top two candidates (Andrea and Brad) are placed on the second ballot.

Second ballot:

26 voters:

Andrea is elected.

### Difference between Runoff voting and Primary Elections

In many voting systems, political parties hold primary elections before the general election. This is not the same as a runoff ballot. In a runoff ballot, all candidates are placed on the inital ballot, and all voters are allowed to participate in the vote.

### Potential for Tactical Voting

This system encourages tactical voting in a manner very similar to plurality voting: voters are encouraged to avoid voting for candidates who do not have a chance to contend for the second ballot. However, this is a lower threshold than contending for the election.

If voters strongly dislike one candidate, they are also encouraged to vote for a candidate who they believe can defeat that candidate in the runoff.

### Monotonicity

If alternative X wins, and the only changes to the ballots are changes that increase the ranking of X, then X should still win. That is the monotonicity crierion.

All runoff voting methods violate the monotonicity criterion, including this one. For example, let's assume the voters' sincere preferences remain static between rounds as follows:

```       8       A>B>C
9       B>C>A
11      C>A>B
5       A>C>B
```
```                       A       B       C
1st Round:      13      9       11
2nd Round:      13      -       20
Outcome:        C>A>B
```

Then say the A>C>B voters change to C>A>B in order to feel like winners, which means that the only change in the profile is that C, the original winner, gets even more support than she had before. C no longer wins first place.

```       8       A>B>C
9       B>C>A
16      C>A>B

A       B       C
1st Round:      8       9       16
2nd Round:      -       17      16
Outcome:        B>C>A
```