CU Boulder upgrades to Approval Voting; could go even further

The recent student government elections at CU Boulder used an improved voting system called Approval Voting. Approval Voting means you can vote for as many candidates as you want, rather than being limited to the number of winners. This is a big improvement over the traditional system called Plurality Voting. Approval Voting ensures you can never be punished by voting for your favorite candidate, and solves the spoiler effect.

Approval Voting is a great way to elect in a single-winner election, e.g. for mayor, governor, senator, etc. But for multi-winner races (e.g. the CUSG Representative-at-large election, with five winners) Plurality Voting and Approval Voting can both produce lop-sided victories.

Consider, for example, the election of the Arts and Science Student Government board members. The Unite party took all five seats, despite earning only 54% of the votes. The Inspire party got almost 45% of the votes, but won zero seats. An arguably more fair outcome would have been three seats for Unite, and two seats for Inspire.

The tables were turned in the University of Colorado Engineering Council elections. Eight of the nine Representative-at-large seats went to Inspire, and only one went to Unite. But Inspire won 67% of the vote. Unite won 33% of the vote, but earned only 11% of the seats. A more fair result would have been three seats for Unite, and six seats for Inspire.

Inspire also swept the UCEC senator elections. There were four candidates (two Unite, two Inspire) running for two seats. Unite won 46% of the votes, but zero seats. Again, this was not a representative outcome. Looking at the results, it seems to me that the winners should have been Inspire's Benjamin Zatz, along with Unite's Rachel Sobke.

Arden Rose, UNITE 348 21%
Rachel Sobke, UNITE 407 25%

Jon Fearer, INSPIRE 430 26% Elected
Benjamin Zatz, INSPIRE 459 28% Elected

So what's the solution? Proportional Approval Voting!

It turns out that a Danish statistician figured out the solution to this problem back in 1890! Imagine if we elect winners one round at a time. Then after each new winner is selected, we "divide" each ballot by w, where w is "the number of winners that ballot has approved, plus one".

As an example, imagine you approved Benjamin Zatz and Jon Fearer:
  • In the first round, your ballot is just divided by 1, which has no effect. Your votes count at full strength.
  • Let's say Benjamin Zatz is the first winner, which he would be based on the actual election results.
  • In the second round, your ballot is divided by 2 (because you voted for Zatz, who won in the previous round). Now your vote for Fearer counts as only 1/2 a vote. This means that all the people who didn't vote for Zatz (i.e. Unite voters) now have the power to elect one of their candidates.
  • This process continues as seats are awarded, providing fair representation to any faction which has enough support to deserve a seat.

Proportional Approval Voting would have produced the kind of fair outcomes we just considered above. The total seats awarded apparently wouldn't have been much different. But the allocation would have allowed Inspire to have a voice in ASSG, and Unite to have a voice in UCEC.

But isn't this complicated?

Not really. Consider that Australia's senate has been elected via the much more complicated Single Transferable Vote system since 1938, far before modern computers or even electric calculators. It was all tallied by hand from paper ballots. Thus Australia has a truly representative democracy. Doesn't CUSG deserve that too?

Here I demonstrate how Proportional Approval Voting can even be tallied using a simple Google Docs spreadsheet.


In summation, Approval Voting is a big step forward for CUSG elections. But it can be even better in the multi-winner races. Proportional Approval Voting is worth considering.

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