Please vote for your favorite movie out of the below list:
A group of a dozen or so friends meet up every Wednesday night for "movie night." At first they decide what movie to see by discussing it via a few emails back and forth on the day of the movie. As the group gets bigger, they decide to start holding web polls so that they can vote on the movie, each time listing all the movies playing in town that they haven't seen yet.
But something starts happening that is bad. One of the members, a hard-core science-fiction fan, becomes frustrated that since the web polls started, he rarely gets to see movies he likes. So he decides to get a bit sneaky. He knows that several other members of the group also like sci-fi movies, so he emails them and suggests they have a separate poll earlier in the week, and decide among themselves which movie they prefer. Then they'll agree to all vote for their movie in the main poll, rather than splitting the sci-fi vote between several movies.
For the next few weeks, the sci-fi movies always win. By organizing to avoid vote-splitting, the sci-fi buffs have attained power. But soon, some of the other members who tend to prefer "chick flicks" catch on to what is happening. They start holding pre-votes as well. Eventually those who are more middle ground find that they really must join one or the other group if they are going to have any say whatsoever.
Over time, it works out that about half the time they watch a sci-fi movie, the other half they watch a chick flick. Each week, about half the people are happy and half unhappy. The group, which used to be fun, now has become polarized and has attained an air of confict and acrimony. The middle ground movies, which almost all the people could be relatively happy with (even if not their very first choice), are rarely if ever seen.
Please vote for all movies in the below list that are acceptable to you:
Eventually, the founding member Judy, sad that the group isn't as fun as it used to be, decides to do something about it. She changes the main poll so that people can vote on multiple movies. Then she simply picks the movie that has the most votes. This technique, called "Approval voting", turns out to be remarkably immune to giving any advantage to those who cluster into groups and hold pre-votes.
Soon, the sci-fi faction and the chick flick faction fade away, since holding a pre-vote accomplishes nothing. Movies tend to be picked that all can enjoy....or in the very worst case, are tolerable to all. And the group becomes fun and harmonious again.
While Approval voting seems to fix the main problem, people quickly notice a problem. They are never sure which movies to approve and which not to approve. For instance, if Jeff's first choice is Aeon Flux and second choice is King Kong, should he approve them both, or only approve Aeon Flux?
Well, it depends on how the others vote. If Aeon Flux and King Kong are the two leaders according to the votes of the rest of the group, Jeff should vote for only Aeon Flux, to help it beat King Kong. If, say, Pride and Predujice is in the lead, he should vote for both of them (as well as all other movies he prefers to Pride and Prejudice).
What it comes down to is Approval voting gives an advantage to those who are best at guessing how others are likely to vote. This is frustrating to those voting, and Judy thinks it seems unfair.
Current standings are shown in blue. You can change your vote until I close this poll, which will happen whenever I please.
Having learned that her little movie club has some geeky (and cut throat) members who are prone to trying hard to out-maneuver the others to get the movie they want, Judy decides to make an improvement to make things more fair. She sets up the web poll so members can see the intermediate results, and can change their vote at any time until the poll is closed. Then she tells them that she will close the poll at a random time, to eliminate any possibility of someone trying to cheat by waiting till the last minute to change their vote.
So now, people vote, then come back and modify their vote as many times as they want if they realize -- based on the current winner and runner up -- that their previous vote no longer seems optimal. They find that it always works out that the election stabilizes after a bit, as everyone finds their "sweet spot".
Judy has not only gotten rid of the polarizing effect they had with conventional voting, but she has achieved perfect fairness. Nobody has an advantage due to being a better guesser at how others will vote, since everyone can actually see how everyone else is voting.
Judy, now fascinated with perfecting her voting system, isn't happy with the fact that her system takes so much effort. She is admittedly thrilled that it no longer seems to drive her movie club into two opposing factions. She likes that it seems to pick movies that have a broad consensus, and that it is now fair to all. But she'd like to make it more straightforward, so that the voters can vote just once, and without having to think about how others will vote.
Please rank the following movies, with 1st being your favorite and 6th your least favorite:
Judy had noticed that, to help with deciding which movies to approve and not approve, most people had started listing the movies in order of preference on a piece of paper. So she decides to let people rank movies (1st choice, 2nd choice, etc) right on the ballot. Then she has a formula* that reprocesses the ballots into the simpler Approval ballots, taking everyone else's ballots into consideration.
Basically, she has automated the whole "come back and tweak" process. She assures everyone that the Approval ballot that is submitted on their behalf is always the best, most strategic ballot...the same one that they would have submitted themselves if they came back and voted over and over using the previous system. Specifically, the system will always give a "yes" vote to all movies that are preferred to the leading movie among the other ballots. It will also give a "yes" to the leading movie if it is preferred to the runner up.
People now have no incentive to collaborate with others, to bother trying to estimate how others will vote, or to vote with anything other than their true preferences. The system does all the work for them, and produces a fair result. And Judy is now satisfied that her voting system is as good as it could get.
*How the system converts the ranked ballots into Approval ballots
There are two ways to convert ranked ballots into Approval ballots. The first is sort of an automated version of the technique described above, where everyone could modify their votes until things stabilized. Here, the system might create an Approval ballot for each voter, simply voting for the top 50% most preferred movies of this voter. Then, while checking which movie is number 1 and number 2, it would continue to adjust ballots until it stabilizes on a single winner and single runner up, and no ballots can be improved. The stable situation in which no ballot can be improved, given the results of the last round, is called an "equilibrium".
Another way might seem backwards, but is actually more straightforward. The system would "try out" each pair of movies as the tentative leader and runner up. The Approval ballots would be generated with that assumption, and if the set of ballots agreed (that is, produced the same winner and runner up), we would consider this an equilibrium. In the extremely unlikely case that there are multiple equilibriums (in other words, we have a tie), a simple formula -- which is beyond the scope of this article -- can break the tie.
And finally....
It should be noted that there are other systems that allow voters to submit ranked ballots, and similarly give voters no incentive to cluster into factions, or to vote with anything other than their true preferences. We chose to describe the above system (which is technically considered a form of "Declared Strategy Voting") because we found it the easiest one to explain. There are various systems that are called "Condorcet methods" which in practice are just as good, and achieve similar effect. Another ranked choice system, "Instant Runoff Voting", is currently in use in real elections in Australia, San Francisco and elsewhere.