Tuesday, May 8, 2007

At Large candidates get no respect (statistically speaking)

Are the official election results misleading citizens about the race for City Council At Large seats?

Doug Linkhart’s 41,555 votes are displayed as representing 41% of the total. But the truth is, he received far more support than that.

That's because the Denver Election Commission displays the At Large percentages as a basis of all votes given in that race. Normally, that's fine. Total votes are usually equal to the total number of voters in any given race. But when voters can select up to two (2) candidates, as happens with At Large seats, the numbers are thrown out of whack.

For instance, the total number of At Large votes in May 2007 was 101,288, so half of that (assuming everyone voted for two candidates) would be 50,644. That seems low, insofar as 65,270 voted in the more obscure Clerk & Recorder race, yet it also seems unlikely that tens of thousands of folks chose just one of the three candidates. Still, if we raise the estimated votecount to 57,000 (halfway between the two numbers), the percentages change quite dramatically.
Doug Linkhart – 41,555 / 57,000? - 72.9% (not 41.0%)
Carol Boigon – 31,952 / 57,000? - 56.1% (not 31.6%)
Carol Campbell – 27,144 / 57,000? - 47.6% (not 26.8%)
Write-In Candidate - 637 / 57,000? - 1.1% (not 0.6%)
Thus, for a more intuitive accounting, the vote tallies for At Large councilors should be judged not by the total number of votes, but the total number of voters who submitted a choice in that category.

Opinions may vary on the need for this revision, but it is at least important for voters to realize that the actual percentage of support for candidates in the At Large race was far more substantial than the generic results indicate.


Andrew Oh-Willeke said...

Another way to present the numbers is the assume that everyone who voted did in fact vote for two, and present the percentage of voters who ranked each candidate last:

Linkhart 18%
Boigan 37%
Campbell 54%

This does a couple of things. First, it illustrates that while Boigan did unexpectedly poorly, that reported in a manner comparable to a one candidate rate, she had a safer lead over campbell than the unanalyzed numbers would suggest -- closer to a 17 point edge similar to that other incumbents managed to ike out, instead of a relatively close 9 point edge.

If you are looking at absolute percentage of voters supporting, as in the original post, it is important to note that "par for the course" (i.e. the percentage you would receive if everyone voted randomly) is 67% if everyone votes twice, and "par for the course" is 56% under the hybrid assumption made.

While the "everyone votes twice" and who was in third place statistic makes the unrealistic assumption that everyone casts two votes isn't precise, its explanation of the data makes more heuristic sense.

Richard said...

This would be an interesting study if we knew how many people double-voted, single-voted or left it blank. Is this information available from the Election Commission?

Also - are results by precinct available from the Election Commission? I can't find results by precinct on their website.

As an aside, I was able to find the election returns from my great-great grandfather's village of Champagney France for last Sunday's presidential election. 82 percent of my distant cousins cast ballots of which 52.78 percent of them wisely voted for Sarko over Sego. It is a shame I can better interpret elections overseas than in my hometown mais c'est la vie.

Andrew Oh-Willeke said...

FWIW, Denver's Mayoral, Auditor, Clerk and Recorder, and Council District elections are all conducted in the French manner, a particularly remarkable thing given that Denver does not have a strong French heritage.