# SCRIRVE

SCRIRVE is a voting system devised by Chris Benham for use with ranked ballots. Truncation is allowed, but in the standard version equal non-last preferences are not. Truncated ballots are first symmetrically completed. Then, working on the reversed profile, repeatedly eliminate the IRV "winner", until one candidate remains. That candidate is elected.

(The name of the voting system is an acronym, standing for "symmetrically complete, reverse, IRV elimination.")

"Symmetrically complete" here refers to a process that is applied to truncated ballots. Each truncated ballot is, as Douglas Woodall puts it, "replaced" by "all possible completions of it with equal weight, chosen so that the total weight is 1." ("Symmetric-Completion" (SC) is a Woodall criterion that says "a truncated ballot should be treated the same way as its symmetric completion.") An alternative description of the system makes no mention of symmetric completion: "Treat truncated ballots as giving equal-last preference to all the unranked candidates. Working on the reversed profile, use ER-IRV (fractional) to repeatedly eliminate candidates until one (who is elected) remains. (Handle equal preferences by splitting them into equal fractions that sum to 1.)"

### Example

Imagine that Tennessee is having an election on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in these four cities, and that everyone wants to live as near the capital as possible.

The candidates for the capital are:

• Memphis, the state's largest city, with 42% of the voters, but located far from the other cities
• Nashville, with 26% of the voters, near the center of Tennessee
• Knoxville, with 17% of the voters
• Chattanooga, with 15% of the voters

The preferences of the voters would be divided like this:

42% of voters
(close to Memphis)
26% of voters
(close to Nashville)
15% of voters
(close to Chattanooga)
17% of voters
(close to Knoxville)
1. Memphis
2. Nashville
3. Chattanooga
4. Knoxville
1. Nashville
2. Chattanooga
3. Knoxville
4. Memphis
1. Chattanooga
2. Knoxville
3. Nashville
4. Memphis
1. Knoxville
2. Chattanooga
3. Nashville
4. Memphis

There is no truncation, so there is no "symmetric completing" to do. To use IRV on the reversed profile, we can begin by looking at the last preferences:

Memphis 58, Knoxville 42, Chattanooga 0, Nashville 0.
Memphis has more than half the last preferences, and so wins the first IRV election on the reversed profile; and so is eliminated (and dropped from the ballots.)

New last preferences tallies:
Knoxville 68, Nashville 32, Chattanooga 0.
Knoxville has more than half the last preferences, and so wins the second IRV election on the reversed profile; and so is eliminated (and dropped from the ballots.)

New last preference tallies:
Nashville 32, Chattanooga 68.
Chattanooga has more than half the last preferences, and so wins the third IRV election on the reversed profile; and so is eliminated. The one remaining candidate is Nashville, so Nashville is the winner.

Things are more simple when there are only three candidates. In that case, SCRIRVE elects the winner of the pairwise comparison between the candidate with the fewest (fractional) last preferences (or the fewest on the symmetrically completed ballots); and the winner of the pairwise comparison between the other two candidates. If the three candidates are in a cycle, then the winner is simply always the candidate with the fewest (fractional) last preferences.