Approval Voting is better than Plurality Voting, even in multi-winner races

There have been some cases where Approval Voting, which is ideally intended as a single-winner voting system, has been criticized when used in multi-winner "at-large" elections. The gist of it is, suppose you have the following scenario:

Voters are roughly split into three groups: left, right, and center. There are three candidates from each of those factions (i.e. nine total candidates), and we're electing three winners.

The critics will argue that a reasonable outcome would be one that is proportional, such that you get one winner from each faction.

Approval Voting will tend to elect all three centrists, which is less representative. Although note that this still gives a body with the same ideological center as the electorate, which is crucial.

While this is true, and is a fine argument for favoring Proportional Approval Voting over ordinary Approval Voting, it certainly doesn't favor at-Large Plurality Voting. That system could easily give you two leftists and a centrist, or two rightists and a centrist—a result which creates a body whose ideological center is significantly divergent from that of the electorate.

Incidentally, here's a video demonstration on how to tabulate Proportional Approval Voting in a spreadsheet, with a few simple formulas.

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