Dartmouth adopted approval voting in 1990 to fill vacancies as they arose on its Board of Trustees. [Dartmouth has 18 trustees. The procedure during 1990-2007 was for them to be elected in single-winner elections when a vacancy needs to be filled, from 3 nominees selected by Council, plus however many more satisfy petition requirements. Apparently over 20000 voters typically participated.] But as of 2007 , it appears from this report (pdf) that Dartmouth is about to abandon it to go back to plurality voting. Why?
Well, frankly, the reasons given in the report make no sense to us, and some of the claims there are false:
Specifically, if all ballots approved either 1 or 2 candidates, there must have been 19% approve-1 and 81% approve-2 ballots. Norman in later email later hypothesized that actually there may have been a strategy of "either voting for the petition candidate or voting for all [3 opposing] nominated candidates." If that was the only thing going on then 60% of the votes would have been approve-1 and the remaining 40.5% approve-3s, but in this case approval voting was clearly showing its immense value by preventing an enormous "vote-split" among the 3. In any case the fraction of "approve≥2" ballots presumably had to be somewhere between 40.5% and 81%.
Nevertheless, apparently all that made sense to the brilliant individuals making voting recommendations for Dartmouth. We suspect that the Dartmouth voters would be less likely to countenance e.g, abandoning choosing valedictorians via grade-point averages and switching to "each professor names one student" plurality voting. (Well, we know they would be less likely, since count the number of years this system has been operating without any such proposal.) In other words, range voting would seem less likely to lead to a backslide.
Although the Trustees stopped using Approval Voting as described above, the Students (who'd previously used IRV) switched to approval voting to elect the student body president (and also vice president) starting with the 2011 election.
Here's what happened in their 2011 presidential election. (We thank Harry J. Enten'11, who did the counting, for this data.) First of all, the election was quite strange because only one candidate, Max D. Yoeli'12, was "on ballot" with two other major candidates, William R. Hix'12 and Aaron R. Limonthas'12, both running as "write-ins." Hix was ineligible to run on-ballot under EPAC rules due to a previous suspension; Limonthas ran from home in Texas, since he was not living at Dartmouth (an "off term") at the time. To add to the strangeness, the student newspaper reported some wrong numbers, overstating Hix's and Limonthas's approvals (although it got the winners correct).
| #approvals | Name | Status |
|---|---|---|
| 691 | Max D. Yoeli'12 | On-ballot, and winner |
| 622 | William R. Hix'12 | Write-in (disqualified from on-ballot due to suspension) |
| 377 | Aaron R. Limonthas'12 | write-in, not on campus at time |
| 18 | Benjamin B. Ludlow'12 | write-in |
| 13 | Maya S. Granit'11 | write-in |
| 10 | Eric R. Olson'12 | write-in |
| 6 | Brandon T. Aiono'11 | write-in |
| 5 | Matthew M. Heffley'12 | write-in |
| 5 | Amrita Sankar'12 | write-in (won separate vice president election by landslide) |
| 4 | Sahil V. Joshi'13 | write-in |
| 3 | Eric L. Ramsey (Student Act/Collis) | write-in |
| 3 | Brian B. Holekamp'12 | write-in (also placed second in separate vice president contest) |
| 3 | Justin E. Lashley'12 | write-in |
| 2×10 | 10 other write-in candidates got 2 approvals each | write-in |
| 1×96 | 96 other write-in candidates got 1 approval each | write-in |
| 1876 total approvals | 119 total candidates | 1665 total ballots |
The Dartmouth 18 April 2011 (article by Tina Ma) says "A total of 1,665 ballots were cast in the presidential race, which represents the lowest voter turnout in the past three years, according to EPAC chair Harry Enten '11."
1564 ballots approved at least one among the "big three." Restricted to the top 3 candidates only, the ballots were as follows:
| M.D.Yoeli | Wm.R.Hix | A.R.Limonthas | ∅ | {MDY,WRH} | {WRH,ARL} | {MDY,ARL} | {MDY,WRH,ARL} |
|---|---|---|---|---|---|---|---|
| 613 (of total=691) | 533 (total=622) | 300 (total=377) | 71 | 41 | 40 | 29 | 8 |
Yoeli probably would have been the plain-plurality voting winner too, but it is mathematically possible that it would have been Hix, e.g. if enough of the 41+8=49 Hix-and-Yoeli both-approving voters plus enough of the 40 Hix-and-Limonthas approvers would have voted Hix if forced to choose only one (and if not too many of the 29 Yoeli-and-Limonthas approvers would have chosen Yoeli). The 71 voters who approved no big-3 candidate, and the 8 who approved all three – 79 (4.7%) in all – were unable to influence the race among them. However even if they'd all voted for Hix, that would not have been quite enough to make him win, so they could not have changed the winner.
If Instant Runoff or any other full-ranking-as-ballots system had been used, this election would have been a disaster in the sense that each voter would have had to provide a full rank-ordering of 119 candidates (if all the write-ins had been included) – or actually that would have been impossible, in which case a restriction to only the on-ballot candidates would have meant the "election" had only one candidate, which would have been an even worse joke. Top-3-only bastardized IRV would have been feasible, but would have placed write-ins at an artificially-severe disadvantage (well actually, they already were disadvantaged, but IRV3 would have made it more severe by causing vote-splitting effects among the write-ins, which they did not suffer with approval voting). IRV3 probably would have elected Yoeli, although again, there is a slim chance it wouldn't.
(Information about the 2006 student president election conducted via IRV, and about the next two approval elections.)
For range voting we have recommended that the candidate with the greatest average win. If we regard the approval system used here as {0,1} range voting (i.e. with only 0 and 1 as permitted scores) and if candidates left unmentioned by voters were regarded as literally, "no opinion" votes, then plain-averaging would have got into trouble by electing some unknown write-in. It is for that reason that average-based range voting with "no-opinion" scores permitted, is recommended for use with a quorum rule (and if write-in candidacies are permitted, this seems essential). In the present case, if we had used the "soft quorum" method of giving every candidate 60 "artificial 0 pseudoscores" before voting started, then Yoeli still would have won with all the low-approval write-in candidates left in the dust??
More will be added later?? #approved histogram? #total ballots? spoilage rates? Election admin problems? More previous Dartmouth elections? What did Yoeli, Hix, and Limonthas think of the election method?