How are Chris' "surplus votes" redistributed after counting first choices?

In actual choice voting elections, not many votes will ever be categorized "surplus" votes. Few, if any candidates, will win with
first choices alone, and most ballots move to next-ranked choices only
when the higher-ranked choice candidate has been defeated. However, the
video's example with Chris shows that it is important to have a fair way
of distributing "surplus" votes.In the video, Chris is a popular candidate who is the first choice of 16 out of 31 voters. That means a majority of voters supported her as a first choice. If we left those votes with her, the remaining 15 voters would determine the two other winners -- violating the principle of majority rule.

Here's how choice voting upholds the majority rule principle. Given that Chris needs eight votes to win and has 16 votes, half of her votes are needed to elect her and the remaining half need to be allocated to voters' next choices. Although there are slight variations in the rules, there are two basic methods of allocating surplus votes.

__Method one: "Whole ballot" allocation__

In elections in cities like Cambridge, Massachusetts, election officials only deal with "whole ballots." That means a ballot's value is always one. In our example, then, eight of Chris' ballots would continue to count for her in the second round of counting because eight is the victory threshold. In this second round, however, eight votes would now be counted for the second choice candidate indicated on that ballot.

Cambridge uses a "random distribution" method of distributing surplus votes. Ballots are counted in order of neighborhood. As ballots are tallied, each one is given a number -- the first ballot counted for Chris is given a "1", the second ballot counted for Chris is given a "2" and so on. If half of Chris' ballots need to count for next choices in the next round of counting, then every other ballot cast for her would be "transferred" -- that it, it would count for that next choice candidate in the next round. Although the choice of which ballots move onto next choices is random, it is guaranteed that the ballots counting for second choices will be evenly distributed across the city in exact proportions to where she earned first choice support..

In a 1955 city council election with choice voting in Cincinnati, there were hundreds of thousands of votes, but the final winner was only a handful of votes ahead of the final losing candidate. They held a recount, starting over with a new "random distribution" of votes. The results were nearly exactly the same, showing how well this method works.

A variation of the whole ballot method is to first count all next choices on each ballot and then make sure that ballots are distributed to next choices in that exact proportion.

__Method two: "Partial ballot" allocation__

In the partial ballot method of redistributing surplus ballots, ballots cast for a candidate surpassing the victory threshold are divided into two values. Every ballot is counted in part to elect the winning candidate and in part for the next choice indicated on that ballot. That means every ballot is treated equally. In our video example, then, half (0.5) of every one of Chris' ballots would count for her and half (0.5) would count for the next choice indicated on her ballot.

The partial ballot method is particularly appropriate when the choice voting count is being carried out with a computer program. Although the whole ballot method is fair and well-tested, the partial ballot method is precise in assuring that every ballot is treated equally.