Thursday, June 10, 2010

Valid ballot - What does it mean for IRV?

IRV is sometimes criticized as being too complicated for voters to understand. To prove that this is not a problem, proponents like to point out that the percentages of invalid ballots for IRV elections are usually low, usually between 0% and 1%. So what does it mean to have an invalid ballot in an IRV election?

Strictly speaking, the answer lies in the rules for each locality. However, it is common for a valid IRV ballot to be judged effectively by one rule: there must be no overvote in the first ranking of each race. Let's take a look at some valid and invalid IRV ballots:

click to expand

Only the first ballot above was marked by a voter fully understanding and utilizing IRV. But a single vote, as though IRV were not in use, is perfectly acceptable. So is a blank race, same as in a non-IRV election. The duplicate vote, in which one candidate is voted for twice, is unique to IRV. This is considered valid under the assumption the highest ranking vote is the intended vote. An overvote, selecting more candidates than allowed, is invalid for a non-IRV election. But in IRV as long as one "good" vote can be collected, the race is usually considered valid. Therefore an overvote in the highest rank is invalid, but overvotes in lower ranks are usually valid. For example, the bottom-left ballot shown above has an overvote in the second rank, but the first rank vote is still counted,

Valid IRV ballots still can signify voter difficulty

A common rule for treating duplicate votes and overvotes in IRV is to count votes until the duplicate or overvote is reached, and then "exhaust" the race. In the "Overvoted IRV second rank" ballot shown above, the ballot would be counted for Candidate 3 in the first IRV round, and then exhausted (no longer counted) in any successive rounds.

No first rank overvotes should be found if a ballot scanner is used to accept and check cast ballots. The overvote would be detected and the ballot returned to the voter. This ballot would be spoiled and the voter would be given a new ballot and a chance to try again. A way to gauge this is to look at the spoiled ballot count for elections.

Ideally, no overvoted or duplicate voted ballots should be cast at all. They should all be caught at the precinct and the voter allowed to revote. IRV has the "advantage" that these ballots can be accepted and counted until the problem rank is reached. But in many cases the voter has made perfectly valid choices in ranks after the problem rank, yet with IRV these votes are never used.

Aspen: Beyond invalid ballots

The news story IRV passes first test about Aspen's first IRV-based election on May 5, 2009 tells us "There were 16 people who skipped the mayor’s race and 23 who cast “invalid” ballots in the council race." We also find no invalid ballots in the Mayor race and 34 who skipped the City Council race. This is out of 2,544 ballots.

The Aspen Mayor race had 4 candidates. There were 1188 fully ranked ballots (46.7%), 278 ballots ranking 3 candidates (10.9%), 512 ballots ranking 2 candidates (20.1%), 542 ballots ranking 1 candidate (21.3%), and 16 ballots ranking 0 candidates (0.6%). We also find 26 ballots with overvotes or duplicate votes, 1%. But there are no invalid ballots only because none of the overvotes are in the first rank.

In the City Council race, with 9 candidates, we find 719 fully ranked ballots, 28.3%. It comes as no surprise that some people have limits in how many candidates they feel like ranking. They don't have to vote for anyone really, and 16 did just that. In between the 719 fully ranked ballots and the 16 completely unranked ballots we will find some with 1 candidate ranked, 2 ranked, etc. Also there were 128 ballots with overvotes or duplicate votes, 5%. In this case 23 of the overvoted ballots had overvotes in the first rank, and were considered invalid. For what it's worth, those 23 voters may have simply tried to vote "the old way", marking their two council candidates of choice in the first column.

We mentioned spoiled ballots, those that were rejected at the poll, giving voters a chance to vote a new ballot. In Aspen's IRV election there were 168 of these, far more than usual. The 148 ballots with duplicate votes or undervotes in at least one race should have been caught at the precinct so those ballots could have been spoiled and revoted. But the precinct AccuVote-OS equipment was programmed only to check the first rank for Mayor and the first two ranks for City Council. And it was unable to deal with "messy" ballots in which the first few ranking are blank, but later ranking have votes. It let invalid ballots slip through, to be rejected later, only after the voters had gone home. Also, the AccuVote machines are completely unable to detect duplicate votes.

Overall, about 316 Aspen voters (168 + 148) had some kind of trouble with a ballot, 12.4% of them. It would be more useful to look at those statistics, rather than just say that only 23 ballots were invalid. We need to look at a more complete picture when assessing how well IRV is working for the voters.

UPDATE 6/11 10:50 AM: A problem was detected in my algorithm for finding duplicate votes. Those numbers have been corrected, resulting in higher counts.

UPDATE 6/11 1:56 PM: The spreadsheet with election results and analysis is here (right-click and save-as aspen_irv_checks.csv). Or download the XLS here.

UPDATE 4/22/2011: I wrote about the Aspen 2009 Mayor race: "We also find 26 ballots with overvotes or duplicate votes", but that should not be taken to mean that those ballots were discarded, altering the count. While that could have happened and in some elections it does, in this particular case none of those mistaken marks had any effect on the Aspen Mayor race because choices in higher ranks prevailed.


  1. It should be noted that over 7% of the mail in ballots contained over-votes. There was no opportunity for the voter to correct those. In a close race, like the CC seat 2 race, such high error rates can obviously impact the outcome of the election.
    In many ways, IRV in Aspen did not reflect voter intent as was intended.

  2. I should have also stated that this high error rate occurred in a municipality with a very high education rate. In a recent (unscientific) poll, close to 80% of the Aspen residents had at least a 4 year college degree. I would think that this is far from typical compared to many cities which are considering IRV.


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