Ranked-Pair Voting (Discussion)

The anecdote I've always use in favour of ranked-pair voting is fairly simple, and with a slight modification to remove party names is as follows:

Say you have 9 candidates standing for election, 8 left wing and 1 right wing. The right wing candidate gets 20% of the vote. Each of the left wing candidates gets 10%. By a basic plurality (First Past The Post - vote for one candidate, most voted candidate wins) the right wing candidate takes the seat, despite 80% of the populace voting for candidates that are opposed to them. With ranked pairs, the right wing candidate will almost certainly come last, as they will be ranked last by 80% of the voters.

My usual illustration is the Conservative Party winning over SNP/Green/Labour/etc, as I'm in Scotland. But in short, one-person-one-vote can leave you discarding the votes of a supermajority. Ranked pairs means the most popular candidate always wins. After all, if there's three people running for a post, and half of the voters want A, half want C, but they can all agree on B being a second choice, surely B should win?

Thank you both for the explanations and I certainly see benefits to the ranked-pair voting compared to the 1 person 1 vote system. But one of the points that Euan makes is one I would actually consider a point against using it. Here is my example:

If we take the ranked-pair system with four candidates and use our current scoring system then the following situation could arise:

- 25% votes A, C, B, D
- 25% votes B, C, A, D
- 25% votes D, C, A, B
- 25% votes D, C, A, B

There are of course numerous other possibilities, but the above one is not a very strange possible outcome. So let's sum up the scores (Where I will pretend that a hundred people voted): A gets 25*3+25*1+25*1+25*1=150 points. Candidate B gets 25*1+25*3+25*0+25*0= 100 points. Candidate C gets 25*2+25*2+25*2+25*2=200 points. Candidate D gets 25*0+25*0+25*3+25*3=150 points.

So according to this election the results are:

Candidate C: 200 points (winner), favoured by nobody
Candidate A: 150 points (runner-up together with D), favoured by 25%
Candidate D: 150 points (runner-up together with A), favoured by 50%
Candidate B: 100 points (last place), favoured by 25%

Do you see the problem here? Although 50% favoured D, that candidate only has a shared second place, while C, favoured by nobody, actually wins. Yes, of course all people thought C a good runner-up and apparently many thought D a bad candidate (if two candidates take very different stands on certain points this could actually happen), but the fact remains that in this case it would seem that the votes of 50% of the people aren't enough to make their candidate win. You could say that with C as the compromise for all, everybody wins, but you could just as easily say that nobody wins.

If you have a 1 person 1 vote system this problem would not arise: the person with the most votes would win. True, this does mean that with two opposing candidates there could be a significant group of unhappy people, but the fact of the matter is that you do have a person in charge who has the majority of the votes.

This all is under the condition that the winning candidate would be unable to decline their office after the election results (why is that an option, by the way?). The only option then would be to have new elections which, as Robert pointed out, is a lot of work but in my eyes the most democratic way to go on.

Don't get me wrong: it's not that I am very much against ranked-pairs, but to me the 1 person 1 vote system just seems to be a little more effective in the way that you get the person in office who has the majority of the votes (again under the condition that this person cannot decline office all of a sudden).

This may be a funny thing to say: but isn't this something that our members should vote on? If that has already happened at one point (I must admit that I cannot remember) then this discussion is of course a bit pointless (although it's always important for people to understand how the voting process works exactly). But if not, then maybe all members should vote on this (voting on how to vote: I know...)?

-Mischa

There are of course more pandas in Scotland than Conservative MPs...

A couple of years ago our country had a referendum on changing the voting system for Parliamentary elections from FPTP to the Alternative Vote; it got defeated by over a 2-to-1 majority (for the record, I voted No). However, we're not electing a multiple member chamber with party allegiances, we're electing a 'president', as it were.

Personally, I would favour a run-off ballot - it ensures that the victor is the clear choice of the top two candidates.

(Except in Italy, of course. In Italy, no one is ever happy with the outcome of a vote.  Not even the winner.)

Again a good explanation, Robert and I certainly can't argue with the mathematics (and no, I have no idea what a Nash Equilibrium is). But there are two things that come to mind.

The first has nothing to do with statistics whatsoever, but more a question of heart and it is based on the statement (whether this is true every one shoud decide for themselves) that 'with a compromise nobody is happy; you don't have winners, only losers.' Now this is way more strongly put than I'd feel, but the fact of the matter is that people want to see 'their' candidate win. They might be okay with the person winning that they voted in second place, but they will feel disappointment because their candidate didn't win. The question you should then ask is: what is worse? a majority of people who didn't see their number 1 win, but are only mildly disappointed because their number 2 made it? Or a large group of people (probably, but this certainly doesn't mean a majority!) who are very happy because their number 1 has won while the rest of the people (which may be a majority of the total number) are (mildly or very) disappointed?

The second issue is that I suspect that a lot of people have a favourite candidate and don't care so much about the rest. They'll put their favourite on top of the list but the other three will be put in a random order. So my question here is: would it be possible by coincidence that because of this voting behaviour a candidate will be positioned on place number 2 on the list so many times that this candidate might actually win, not because the candidate was favourite number 2, but purely because of coincidence (remember that we don't have a very large group of voters). Or are chances of this so small that we can ignore this possibility (this is not some type of warning: this is an actual question)?

-Mischa

For a person in the second position to beat someone in the first position (ignoring the votes for these candidates outside these respective positions), they need over 50% more people voting them to the #2 position than the people voting the person in the first position to the first position.

Now assuming people are robots, that campaigning does nothing to impact the votes of the people and likewise the Q&A, and also knowledge of each other, and assuming that your worries involve a simple majority already being set on the winner (aka a more than 50% of the voters having chosen the same person for the #1 position, and that all of the voters randomly chose the same person for the #2 position enough times that the person in the #2 position beats the person in the #1 position, the odds are less than 5 out of 216 of this happening, or less than 2.3148148...

That's referring to a Ranked-Pair election with 4 candidates. Mind you this is horribly inaccurate, the odds should be much smaller because campaigning, the Q&A, personal records, etc. all play a role in decision-making. The above figure is assuming people only care about the #1 position and have absolutely no opinion on every other person such that they're willing to disregard all information that they could use in deciding their 2nd choice which is statistically significantly lower as well.

Point being the odds really aren't high enough to raise concern, and if it does happen our government allows for the removal of elected candidates with another vote so if the people really don't like it they can go simple majority and out the person in power if they want.

~Robert

Well again this is greatly simplifying the intricacies of Ranked-Pairs. If we hold a 2-person election to be the epitome of democracy then it should be understood that adding more candidates dilutes democracy under basic plurality - the voices of the biggest few are all that matter. Ranked-Pairs doesn't have this problem, it's effectively several 2-person basic plurality elections rolled into one - the actual number of elections, where "n" is the number of candidates, is n(n-1). There's no dilution of democracy.

You have to understand that in, say, a 4 person election that it only takes 25%+1 vote to hold a "majority" and win an election which means 75%-1 vote of the people will be unhappy. This isn't democracy, democracy is majority "consensus" which isn't actually acquired by 26% of the people saying "we're right because we agree more than you guys do" (that's a system of government where like-minded people rule which isn't democracy). Ranked-Pairs has built-in consensus (it establishes what people are willing to come to terms on and then determines the winning side based on what consensus holds majority) and elects a person based on majority consensus which is democracy.

It might be appropriate to observe, by the way, that if someone does hold a majority of 1st positions (50%+1 vote) yet the 2nd place person actually holds the majority consensus, that democracy does dictate that the latter person actually win by nature, but better than that as I mentioned you can break down Ranked-Pairs into several basic plurality votes and with that you'll see that the reason the 1st place person doesn't win isn't because 2nd place holds a bigger majority but rather that the 1st place person has more people who dislike them than the person in 2nd place.

It's a complicated thing to talk about if you don't look past the surface, the votes assigned per slot on a ballot, but it may be easier rather than look at it as "who do people like the most" and instead look at it as "who do people dislike the least". "Dislike the least" is why the person most voted in the #2 slot should win in instances where Ranked-Pairs says #2 slot holds majority consensus over the most voted for #1 slot. #1 won a majority of people absolutely but succeeded in having the total opposite effect on a very large number of people as well which is why even though the person in the #1 slot received a 55% number of votes to the #1 slot they lose the election because the person in the #2 slot won 95% of the #2 slot votes.

While Ranked-Pairs might have been a touch too complex for Athenian Democracy, it's a more fluid system as evident by the fact that in their days majority consensus was required and a decision would not be made without a majority (thus drawing out debates for long periods of time until they were able to sway the people one way or another).

Even the way I've worded that last suggested sample election, the way we talk about it, we're looking at it in a "cup is half-full" perspective. If I flipped it around and made it "the biggest loser", I'd say the person in the #1 slot was voted off the island by 45% of the voters while the person in the #2 slot was only voted out by 5% of the voters. Do you see my point? 55% of the people say "this person is the best candidate for office" and 45% of the people say "this person is the worst candidate for office" means there isn't really a consensus, whereas for the #2 slot they have 95% of the people saying "this person is a good candidate for office" and only 5% in opposition - this person has the consensus and it's by a majority, so democratically speaking this IS the best candidate, we just didn't have to get there by arguing all day because of the people who are so STRONGLY against the person in the #1 position (it is, as mentioned, only the state by which people cannot agree on a candidate that makes a candidate not a winner).

If we didn't agree on something we'd spend a long time arguing/debating about it until someone gives in (one could say we're doing that now), but Ranked-Pairs recognizes the different points of view, takes into account consensus or the lack thereof and identifies majority consensus.

I'm beating the "consensus" drum a lot but I think that's what you really need to see, it is about agreement that determines the winning candidate which is about recognizing that opinions are more complicated beyond a single favorite, and that utter dislike is another factor. I mean consider for example George W. Bush's first election - his motorcade was egged and that's evidence of a lack of consensus...see what I mean? Majority? Yes. Consensus? No. Basic Plurality is lacking in this way.

~Robert

I'm glad to see a robust discussion about this sort of thing. Ensures democracy.

Ash

Sorry Osprey, I think you have your threads confused. This thread was explicitly for the purpose of discussing ranked-pair voting as the elections involved the process and it was requested that this information be available to be discussed so that people understood what was happening in the elections. The discussion came to a close nearly 2 weeks ago with what seemed to be the satisfaction of all, though Ash had been on LOA and made a final post noting his approval.

I do find this interesting though and the wikipedia article has been instrumental in helping me understand how the process works. It does not, unfortunately, make the election process "faster" because ranked-pair voting is calculated for me in our voting booth where instant-runoff voting is not.

I believe what I'll now do is investigate the differences between instant-runoff voting and ranked-pair voting as there's differences apparent on the surface but I'm very curious as to what would have to happen in a vote that IRV and RPV would have different turnouts given identical ballots.

~Robert

Uh, so how does that happen then? I feel as if some data is missing here (perhaps the other voters results?)

I scanned through the linked PDF, but I didn't see any mention of IRV at all in the Appendices that described why the systems were problematic. Is it named something else in that paper?

-Jason