Are voting options with lots of minor differences prone to being skewed?

Question

Say you're holding a ranked-choice poll with lots of options that can be grouped in multiple ways, does this skew results in any way, or open it up to abuse?

My example is non-political, but this could easily be applied as such:

• Film 1, Location 1
• Film 1, Location 2
• Film 2, Location 1
• Film N, Location 1 or 2

And so on with multiple films, and two locations.

Is this open for intentional gaming (via tactical voting) or unintentional skewing of the results towards a film or location, where the winning result does not match most people's preferences?

Is it possible to avoid this by having two rounds, voting on a location and then a film?

Answer 1

It depends on how you count the votes.

Example result:

Film A, Loc. A: 7 votes
Film A, Loc. B: 1 votes
Film B, Loc. A: 5 votes
Film B, Loc. B: 6 votes

There are different ways to interpret these results.

Single, non-transferable vote

When you look for the option which got the most votes, the winner would be the first: Film A at location A.

Two separate counts for two separate questions

But when you add up all the votes for the same film regardless of location, you get 8 votes for A and 11 votes for B. That's a clear preference for Film B. The reason why no Film B option won is because the Film-B voters don't agree about the location, so the additional question about the location split the B-vote.

Applying the same logic to the location, you arrive at 12 vs. 7 votes for location, so Location A would be the winner.

But is "B at A" really the solution which makes most people happy or at least content with the result?

Maybe some people care more about location than film, maybe some care more about film than location. Maybe the Film A people have a very strong opinion about their movie and would refuse to watch Film B, but on the other hand the film B people don't care much about what film to see but don't want to travel under any circumstances. So "B at A" would make 14 of 19 people unhappy.

What's a better voting system in this situation?

Let's try the instant runoff system, also known as alternative vote, transferable vote, ranked choice voting, or preferential voting

Instead of a single vote, let each voter rank their preferences from 1 to 4. They can also refuse to rank any options they would never accept. After everyone filled out their sheet:

1. Create a pile for each option where you put all votes which ranked that option as #1
2. Remove the smallest pile, and put each of those votes on the pile for the option which is ranked highest on that vote and still exists. When no existing pile was ranked at all, remove the vote completely.
3. Repeat step 2 until only one pile remains. That's the option which makes most people happy.

A at B would be removed after the first vote and the vote redistributed. As we said Film A people hate Film B, so that person would likely have ranked A at A second:

Film A, Loc. A: 8 votes
Film B, Loc. A: 5 votes
Film B, Loc. B: 6 votes

Now B at A is dissolved. We established that Film B people always prioritize location, so their second choice would be A at A:

Film A, Loc. A: 13 votes
Film B, Loc. B: 6 votes

The result is now clear, but for completeness sake, let's also dissolve the last pile. B at B people would prefer A at B because location is so important to them, But A at B is already gone. Location A options are unacceptable to them, so they wouldn't assign any rank to them. So their votes get discarded.

So we end up watching Film A at Location A. It's the option 7 people preferred, 6 people would accept as a compromise and 6 people are unhappy with.

The instant runoff system is considered a very good voting system when choosing between multiple options because it avoids the spoiler effect (e.g. two similar options stealing each other votes so a 3rd candidate who is actually less popular than them wins), doesn't discourage votes for options perceived as underdogs and leads to a compromise most people can agree to.

There are also very few ways to game this system by tactical voting. The answer by origimbo shows a scenario in which the faction with the most first-votes can improve their results through tactical voting, but it requires a very high degree of foresight and perfect cooperation within the faction to pull off successfully. This is virtually impossible in a public vote (but it might work in a parliament with good factional discipline).

So why is this system so rarely used, when it is so great? Well...

• The counting mechanism is not as easy to understand as with other voting systems. This makes people skeptical of it. Actually, all the voter need to understand to vote in this system is "rank the options by your preference" and a good outcome is practically guaranteed, but it seems more complicated, so people are hard to trust it.
• The counting takes time and is prone to errors. The count is also further complicated by how difficult it is to design a fool-proof ballot paper for it. Have the people fill in numbers, and you get arguments between the counters about if that strange scribble is a 1, 2 or 7. Have the people make crosses in different columns and you will have people make multiple crosses in the same one.
• Opposition for purely political reasons. Changing a voting system usually requires consensus by the people who got in power through the old voting system, and changing it can only mean that their chances for reelection get smaller.

But I digress. Let's see what other options we have to interpret these vote results.

Multiple-round Disapproval Voting

One could also argue that the option "A at B" might be an even better outcome, because only 5 people would directly oppose it (the B at B faction), but it's the option only 1 person prefers the most, so you would pay the price to force 6 people to compromise in order to have one person not feel completely left out. Is that fair? Maybe, maybe not. Your call.

There is also a voting system which would bring you to that conclusion: Have the voters vote with a single non-transferable vote for which option they like the least, remove that option, and then repeat with the remaining options until only one option remains.

They would remove (in that order): "B at B", "B at A" and "A at A" so only "A at B" remains.

Approval Voting

And finally look at the system curiousdannii suggested in a comment to the question: Approval Voting. Everyone gets a "yes or no" vote on every option and you pick the option with the most yes votes when they agree on it. In that case our results would look as follows:

Film A, Loc. A: 13 votes ("A at A", "A at B" and "B at A")
Film A, Loc. B: 14 votes ("A at A", "A at B" and "B at B")
Film B, Loc. A: 5 votes ("B at A")
Film B, Loc. B: 6 votes ("B at A")

It would have the same result as the disapproval system: The least hated (but incidentally also least popular) option "A at B" wins.

But there is one problem with this system: It allows to skew the system with tactical voting. When the "A at A" faction anticipates these results, they can refuse to vote yes on "A at B" which would lead to a win for "A at A".

Answer 2

Like virtually all non-random voting systems, ranked choice voting (see Philipp's answer for a list of some alternative names) does have some structural weaknesses in which a voter with prior knowledge of the voting intentions of others can influence the result in her preferred direction by taking actions other than sincerely enumerating her preferred choices in order.

For example, if it is known that popular choice A beats minor choice C, but loses to choice B, it might be worthwhile for some of A's supporters to insincerely list C as first preference to ensure it survives the process longer the B. In other situations the final result could be changed by strategically adding an otherwise irrelevant choice, or it could be found that the best option for a given ranking order might be not to vote at all.

Separating such a vote into two can lead to dependence on the ordering of the two votes if the result of the first vote is announced before the second (which could lead to tactical choices by the organizers), or to the possibility of very unappealing pairs of choices winning if the first result is kept secret.

Editting to add an example:

Three parties, Clever Party, Nasty Party and Nice Party.

True intentions:

• Clever>Nice>Nasty (10 votes)
• Nice>Clever>Nasty (6 votes)
• Nasty>Nice>Clever (5 votes)

Nasty party knocked out with 5 votes versus [10Cl,6Ni] in first round. Nice beats Clever by 11 votes to 10 in the 2nd Round.

With insincere voting:

• Clever>Nice>Nasty (8 votes, real)
• Nasty>Clever>Nice (2 votes, insincere)
• Nice>Clever>Nasty (6 votes)
• Nasty>Nice>Clever (5 votes)

Nice party knocked out with 6 votes versus [8Cl,7Nasty] in first round. Clever beats Nasty by 14 votes to 7 in the 2nd Round.