The instant runoff voting system that the Hugo Awards use for their final ballot (often known as an Australian Ballot) has come in for a fair amount of criticism in its time. People complain that it is too complicated and they can’t understand it. However, we have stuck with it, because we believe that it produces better results. A certain other well known set of awards has always used a first past the post (plurality) system, but it was announced recently that from now, at least for Best Picture, on the Oscars will use an instant runoff system very similar to the one we use. Apparently the folks in charge of the Oscars think the change will produce better results (better here meaning fewer people yelling, “how come that won?”).
Tied in with this decision is the move to expand the nominee list for Best Picture to 10 films. Once you know that, the instant runoff system decision becomes obvious. With first past the post voting it is possible to win with a (1/N) + 1 share of the vote, where N is the number of nominees. With 5 nominees it was theoretically possible to win Best Picture with 21% of the vote; with 10 nominees you could win with 11%, so the chances of an upset win are much greater. The instant runoff system, however, will always produce a compromise winner that is least disliked by all voters.
There is just one problem for the Oscars. The members of the Motion Picture Academy are complaining that the new voting system is too complicated and they can’t understand it. Perhaps we could get some experienced Hugo voters to help them cast their votes.
Let’s take a look at how this would work. First we will agree on one thing:
40% prefer Harry Potter over Star Trek (40% Harry Potter > Star Trek)
60% Star Trek over Harry Potter (60% Star Trek > Harry Potter)
Now let’s add a third movie, but we will keep the above the same (pairwise)
Rank
1 2 3
40% Harry Potter > Angels & Demons > Star Trek
35% Angels & Demons > Star Trek > Harry Potter
25% Star Trek > Harry Potter > Angels & Demons
You can see that 40% still prefer Harry Potter over Star Trek, and 60% (35% + 25%) prefer Star Trek over Harry Potter.
Let’s run this through IRV.
In IRV, the movie with the lowest votes gets eliminated and the voters second choice gets distributed.
Star Trek has the lowest votes, so it is eliminated, thus transferring 25 votes to Harry Potter.
Giving us:
Harry Potter 40 + 25(transferred) = 65
Angels and Demons = 35
Harry Potter WINS!? Even though 60% preferred Star Trek over Harry Potter
Now let’s look at how getting MORE votes can cause you to loose!
Number of votes 1st Preference 2nd Preference
39 Star Trek > Harry Potter
35 Harry Potter > Angels and Demons
26 Angels and Demons > Star Trek
In this example, Angels and Demons is eliminated, thus transferring 26 votes to Star Trek:
Number of votes 1st Preference 2nd Preference
39 Star Trek > Harry Potter
35 Harry Potter > Angels and Demons
26 Star Trek
39+26 = 65 for Star Trek 35 for Harry Potter. STAR TREK IS THE WINNER.
But before the voting, a big push was made by the studio and convinced many people who wold have voted Harry Potter first, to rank Star Trek 1st, and Harry Potter 2nd. They got got 10 MORE VOTES, that would have voted for HP. Look at it now:
Number of votes 1st Preference 2nd Preference
49 Star Trek > Harry Potter
25 Harry Potter > Angels and Demons
26 Angels and Demons > Star Trek
With IRV, the movie with the least number of votes is eliminated. Now Harry Potter is eliminated thus transferring 25 votes to Angels and Demons.
Number of votes 1st Preference 2nd Preference
49 Star Trek > Harry Potter
25 Angels and Demons
26 Angels and Demons > Star Trek
49 for Star Trek 25+26=51 for Angels and Demons. ANGELS AND DEMONS IS THE WINNER!????
This is IRV’s non-monotonicity effect, the anomaly where by voting for your favorite can hurt your favorite. This is well know and admitted by FairVote and has been the subject of a federal lawsuit with more to come. Unless the Academy and Hugo releases the vote totals afterwards, then you can never see if these anomalies happen.
Nothing’s perfect, Bob T. Kenneth Arrow already proved that about voting methods. The one lawsuit out there on “nonmonotonicity” was given a 5-0 heave-ho by the Minnesota Supreme Court.
The logic of instant runoff is the common sense logic that the last-place candidate is out. It would simulate exactly what would happen if you did a series of runoff elections after dropping this last-place candidates.
As you know, Bob…
The Hugo Awards do release the detailed results of our voting. For example, you can look at the details of the 2009 Hugo Awards balloting on our web site. I have yet to see a case of your relatively convoluted example producing a perverse result in the way you describe.
While your scenario is mathematically possible, I think it unlikely. Besides, the minor risk of such a perverse result far outweighs the obvious faults of FPP voting in five-way races like the Hugo Awards.
Instant-runoff elections are also arguably much like what we see every year on American Idol and all other such elimination contests, only set up so that only one expensive public election is necessary to collect the voter-opinion information to support all of the eliminations.
There’s a pretty good three-minute video walkthrough of instant-runoff voting at http://www.youtube.com/watch?v=wqblOq8BmgM
You are right, no voting system is perfect, but IRV is the WORST. Try Range, Approval, or Borda.
It is an undisputed fact the IRV is non-monotonic, in other words, IRV could lead to a situation in which a voters vote for a particular movie (or candidate) harms, rather than helps, that movie ((or candidate).
Reason Minnesota’s case did not go through is that they had no election that showed these harms, it was hypotheical.
As more elections happen, this effect has begun to be shown. Several cities now have on their ballot to scrap IRV voting.
Now the do.
It happened in Aspen. Candidate lost because he got too many votes.
http://theredant.squarespace.com/storage/MichaelMonotoneViolation..pdf
http://www.aspendailynews.com/section/home/136163
But honestly speaking, who care about what voting methods are used when it about movies, etc. But using it in electing officials in a democracy? That’s when it get scary.
The Australian ballot system involves a series of preferences. Voters write a “1” beside their favoured candidate, a “2” against their second favourite and so on.
If you vote for the candidate with the least amount of primary votes, your vote will be allocated to the second choice on your ballot paper that second choice will be counted as your primary vote. This process continues in the same way, dropping of the candidate with the least votes in each round.
The value of this system in awards can clearly be seen in the hypothetical case of an actor being nominated in the same category for their work in different movies. It is quite likely that their potential vote would be split between the nominations (particularly if their work in each film was of a similar quality). Thereby the genuine “best actor” in that category could easily be beaten by a less popular condidate in a first past the post system.
I have lived in Australia for 40 years, and while the voting system did seem strange and cumbersome at first, a clearer understanding has shown it to be far superior to a first past the post system.
Surely SF fans ought to be capable of getting their heads around these minor complexities to appreciate the fairness of the final results?
Tim:
In fact, for the most part, SF Fans — at least those participating in the Hugo Awards voting — are certainly capable of understanding the “complexities” of the system. I’ve been one of the people counting ballots, and I can attest that a few people “bullet vote” (mark a single X with no further preferences, possibly due to confusion over how the system works); such votes are of course counted as a 1 for that choice with no further preferences. Not many ballots are so marked, and I’ve never seen a “donkey vote” (every category on the ballot marked 1-6 in sequence).
There are always people who find any voting system too complicated. WSFS has decided that IRV balances the trade-off between fairness and ease of use.
Of course, anyone who feels strongly enough that the current voting system is wrong and should be changed is welcome to submit his/her proposals and attempt to get them passed. WSFS doesn’t have a Board of Directors; its “government” is in effect an annual Town Meeting of Worldcon members, with every member representing him/herself. You don’t lobby representatives; you try to talk the other attendees into voting your way. That’s retail democracy in action, but it’s rather messy in practice, especially for armchair theorists.