Topic: Ranked-Pair Voting (Discussion)

Okay so as a need for discussion has arisen, here is a thread to discuss Ranked-Pair voting.  smile

So I'd like to illustrate what's actually happening with ranked pair voting, or more specifically what's happening with the current vote for TC.

So for the sake of illustration, we'll assume ranked-pair voting for an election with 4 candidates: A, B, C, and D.

What everyone's seeing is this:

Candidate A
Candidate B
Candidate C
Candidate D

...and you are asked to order them by preference, highest being the one they most prefer voted into office, lowest being the one they least prefer voted into office. (By the way, the voting booth has the 4 candidates set to scramble the order, so odds are the ordering on your ballot will be different from roughly 96% of all other ballots issued - just mentioning this because this is strictly an example and the letters are not meant to be attached to any individual's names)

So you might set yours to look like this:

Candidate C
Candidate A
Candidate B
Candidate D

...and what then happens is the voting booth assigns the following votes:

Candidate C - 3 votes
Candidate A - 2 votes
Candidate B - 1 vote
Candidate D - 0 votes

So I think we can agree that without looking any deeper into this, things LOOK a little arbitrary. Okay, fair enough, so I'm hoping to elaborate a little further and maybe this will make sense.

What's ACTUALLY happening is there are 6 basic plurality votes going on in this single ranked-pair vote. Ranked-pair votes are actually several basic plurality votes happening simultaneously and it's done in such a fashion that it's easy for the voter to do in a short frame of time and it's easy for those counting the votes to do quickly and efficiently also.

What do I mean by 6 basic plurality votes? And what are these 6?

Well here are the 6 votes:

Candidate A vs. Candidate B
Candidate A vs. Candidate C
Candidate A vs. Candidate D
Candidate B vs. Candidate C
Candidate B vs. Candidate D
Candidate C vs. Candidate D

You'll notice that each candidate appears in 3 of each of these plurality votes and that they are put against each other candidate exactly once.

So let's assume you voted this way in ranked-pairs again:

Candidate C - 3 votes
Candidate A - 2 votes
Candidate B - 1 vote
Candidate D - 0 votes

So in the ranked-pairs, this voter said they prefer C to all other candidates, they prefer A only to B and D, and they prefer B only to D. I'll translate this to the 6 basic pluralities so you can see what's happening.

Candidate A vs. Candidate B - Candidate A wins (+1 vote for A)
Candidate A vs. Candidate C - Candidate C wins (+1 vote for C)
Candidate A vs. Candidate D - Candidate A wins (+1 vote for A)
Candidate B vs. Candidate C - Candidate C wins (+1 vote for C)
Candidate B vs. Candidate D - Candidate B wins (+1 vote for B)
Candidate C vs. Candidate D - Candidate C wins (+1 vote for C)

Let's count it up! C got 3 votes, A received 2 votes, B received 1 vote, and D received no votes. That's exactly what just happened in ranked pairs! (Notice: now that you've seen it in this light it's apparent that ranked-pairs captures 6 of the voter's preferences which is the full list of all possible preferences)

So IF we stuck to basic plurality, this voter would have said "C" and if their choice for a candidate wasn't the one everyone else went with then they have no say in who of the other 3 gets to win the election. This doesn't exactly seem fair. We could do elimination, but then we'd have to do multiple voting rounds to determine who gets the position which will take longer which also doesn't seem right. So ranked-pair voting does all of this.

Now realize that the voting power of the individual under basic plurality is 1 vote and every person gets 1 vote. The voting power under ranked-pairs (in this instance) is 6 votes and everyone has 6 votes. Where this is different though is that if their first choice doesn't win, they still have some say over who gets into office after that.



-pause-



So ranked-pairs can be viewed in a different light, namely that it is 6 basic pluralities happening at the same time. This is convenient because it gives us the full spectrum of the voter's opinions, pitting each candidate against each candidate once and over 1 vote. You can accomplish the SAME results a few different ways:

  • Elimination: you hold a number of votes equal to one less than the number of candidates, each time the voters choose who they DON'T want to win (with the option in the last round of voting for who you DO want to win). Elimination in this example would take 3 rounds of voting but would still accomplish an ordered set of preferences since this voter would vote out D first, then B, and then A (except if their choice doesn't match the majority and then we will not see all their preferences). In this example, the voter can declare no more than 3 of their maximum 6 preferences for candidates.

  • Ladder: as in sports, they tend to put only one team versus another team and then the victor goes on to play another victor. You could do the same with elections, choosing pairs of candidates to go head-to-head. So for instance, if the vote was A vs. B and C vs. D, this voter would say A and C, and then in the second voting round vote C which still establishes a ranked-pair (except we never learn whether they preferred B versus D and to what extent they preferred A to D and C to B, so it doesn't actually supply us with complete information of their preferences). In this example, the voter declares exactly 3 of their maximum 6 preferences for candidates.

  • Primaries: this is mostly similar to a Ladder except that it generally provides even less information because candidates are grouped based on certain identifiable characteristics (i.e. by political party) and then it's votes based on a pool of at least 2 candidates (were it only 2 in each pool then it would be a ladder) and then the final tete-a-tete. In this example, the voter can declare no more than 3 of their maximum 6 preferences for candidates.

Each of these requires multiple voting rounds, and they don't always give us complete information about an individual's preferences. It's of note that basic plurality identifies only 3 of the maximum 6 preferences (in the given example, that they prefer C to all other candidates).

Ranked-pair voting consistently gives all of the preferences of each person on the full spectrum of candidates. It does so fairly and quickly and it gives the person some say in who gets office if their first choice isn't the majority choice (that's a stab aimed at basic plurality).



Here's an example in opposition to basic plurality. Let's say there are 3 candidates, X, Y, and Z, and there are 2 candidates that are highly popular, say X and Y. People in favor of X and Y are so fixated on those two candidates, they don't remotely suspect Z would even win. Think something along the lines of elections in the US: we have Republicans and Democrats one of whom always wins (maybe one day the US will break the vicious cycle), and then a few other people that most voters think won't win.

It's entirely possible in basic plurality that the voters in favor of Republicans and Democrats squabble among each other so much that they ignore the possibility of a candidate winning that is neither Republican nor Democrat who both consider to be a REALLY REALLY BAD choice for President (I won't try to come up with a party that the Republicans and Democrats would both hate more than each other, but I'm sure your imagination can come up with something), and that they ignore the possibility so much so that their votes wind up the minority and this really really bad President takes the White House.

In the above example, ranked-pairs would give the Republicans and Democrats the ability to say "I want my party to win, but I'd rather have a Democrat in office than this REALLY REALLY BAD OTHER GUY!" If the Republicans and Democrats agree that they'd rather have their rival party win than this third candidate, then they may rally together and hold majority to dodge a really nasty bullet that is this third party candidate they really strongly dislike.

So I guess ranked-pairs could serve to aid in compromise by allowing us to say "I'll settle for ______ if the person I really want to win doesn't win", and it also makes it easier to determine tie-breakers (examining who has the higher concentration of votes in-favor).



While this thread is supposed to be for "discussion", I feel my above explanation might put a damper on such a notion, so I'd like to make an inquiry as to whether we'd prefer another system, i.e. elimination, ladder, or primaries (assuming we can figure out some sort of system for grouping people)? And maybe with what reasons you feel another system would be more beneficial? Or contrariwise, if you'd like to make mention against a system please feel free to do that as well.

After my above explanation, I think it's apparent that basic plurality is lacking when there are more than 2 candidates, so I think it goes without saying that I'm against basic plurality when there are more than 2 candidates but you're welcome to your opinion of course.  smile



I will say though that a major problem with doing basic plurality in our existing system is that we allow for a candidate to decide, having seen the election results, to decline their office. In basic plurality there are two ways to handle this and they're both bad:

  • Take the runner-up: that's giving one person (the winner of the election) the power to say "thank you for the votes, but I'm going to throw away the majority of the votes which means only the people that didn't vote for me have say". Currently our legislature says the runner-up is next which works well for ranked pairs but not basic plurality.

  • Re-vote: obviously this is the most democratic way of handling things but it's quite time-consuming.

Effectively with ranked-pairs, we already have enough information on the ballots to recalculate the winner if one person withdraws so a re-vote isn't necessary and the runner-up is already a close match. We don't have it in our legislature that a recalculation is needed if someone steps down partly because that takes a fair bit of record keeping and calculating on the part of the EVC but statistically speaking we aren't taking a very large hit to our numbers, very significantly less of a hit anyways than what we would be taking under basic plurality (if anyone wants to know precisely what % of a hit it is, I can calculate that and probably will do that over lunch now since I'm intrigued).

~Robert

http://i41.tinypic.com/2q2e0ig.png

Thumbs up +1 Thumbs down

Re: 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?

Re: Ranked-Pair Voting (Discussion)

Well said Euan!  smile

I would really like to see ranked-pairs being more common in real-world elections because it always leads to a happier majority than basic plurality. It may not lead to the happiest possible minority as basic plurality can, but it always leads to the happiest majority.

~Robert

http://i41.tinypic.com/2q2e0ig.png

Thumbs up +2 Thumbs down

Re: Ranked-Pair Voting (Discussion)

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

http://i13.photobucket.com/albums/a281/hollyzuzu/6bd9dace-1d9f-469e-b069-b872b1d826dd_zpswfifvw2x.jpg

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

If someone has a clear majority of votes they still win ("first choice" votes). It's only when someone doesn't have a majority backing that we need look at second choices, at which point we've already shown there's no candidate the majority are behind so it's all about finding the best compromise.

Re: Ranked-Pair Voting (Discussion)

Euan Reid wrote:

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?

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.

Re: Ranked-Pair Voting (Discussion)

Mischa Brendel wrote:

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

Actually I don't think this is a problem, I think you're envisioning "least favorite" to be something like neutrality where it could indeed be "strongly against".

So D shouldn't win because 50% of the people fall in the spectrum of opinions ranging from "D's the least qualified" to "D's the devil incarnate" - I should certainly hope nobody actually thinks the latter of any of our candidates, but still keep in mind that those votes way at the bottom are an anchor. These are people who are saying "we'd be happier with anyone BUT D". Logically the math dictates that D cannot win because these people feel so strongly AGAINST D. So you can see it's not just votes FOR a person, it's also votes AGAINST a person that determine the winner.

And you do have it right, it is C that will win in a Ranked-Pair election.

So in a 4 person vote think of the weight in your ranking being thus (it's mathematically equal to the standard ranking as you indicate 3, 2, 1, 0)

+3, +1, -1, -3

In this way, a net score of 0 means they actually only have a 50% approval rating. (you'll notice these numbers aren't arbitrary, they're all determined by differences of 2 conveniently so that the average of them is 0 and so that they're all whole numbers - you could divide them all by 2 and it wouldn't change things, it's just easier working with whole numbers)

So 1st position is "I want this person to win", 2nd position is "I like this person and if they win I'd be content", 3rd position is "I don't want this person to win" and 4th position is "I might grow a beard protesting if this person wins".

So for the same vote we have:

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

And so we have A = 3x25+(-1)x25+(-1)x25+(-1)x25 which gives A=0, B = (-1)x25+3x25+(-3)x25+(-3)x25 which gives B=(-100), C = 1x25+1x25+1x25+1x25 which gives C=100, and D = (-3)x25+(-3)x25+3x25+3x25 which gives D=0.

So we have C as the victor because they're the only person that actually has an above 50% approval rating because they have the only positive score (in fact they have a 75% approval rating) whereas no other candidate has better than a 50% approval rating, so logically C is the best choice for everyone.

Ranked-Pairs actually can be shown through Nash Equilibrium too. If you're familiar with economics enough to know what Nash Equilibrium is, then Ranked-Pairs produces a winning candidate found at the Nash Equilibrium of an election.

It doesn't mean that anyone got their FAVORITE candidate, but it does mean that all of the voters are the happiest possible with the outcome of the vote (debates on the voting system aside that is).

~Robert

http://i41.tinypic.com/2q2e0ig.png

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

RLongtin wrote:

it does mean that all of the voters are the happiest possible with the outcome of the vote

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

"My faith protects me. My Kevlar helps" - (Jim Butcher)

Thumbs up +4 Thumbs down

Re: Ranked-Pair Voting (Discussion)

I... I.... I have a belly button

^^ Lost and confused as per norm^^

Re: Ranked-Pair Voting (Discussion)

RLongtin wrote:

Actually I don't think this is a problem, I think you're envisioning "least favorite" to be something like neutrality where it could indeed be "strongly against".

So D shouldn't win because 50% of the people fall in the spectrum of opinions ranging from "D's the least qualified" to "D's the devil incarnate" - I should certainly hope nobody actually thinks the latter of any of our candidates, but still keep in mind that those votes way at the bottom are an anchor. These are people who are saying "we'd be happier with anyone BUT D". Logically the math dictates that D cannot win because these people feel so strongly AGAINST D. So you can see it's not just votes FOR a person, it's also votes AGAINST a person that determine the winner.

And you do have it right, it is C that will win in a Ranked-Pair election.

So in a 4 person vote think of the weight in your ranking being thus (it's mathematically equal to the standard ranking as you indicate 3, 2, 1, 0)

+3, +1, -1, -3

In this way, a net score of 0 means they actually only have a 50% approval rating. (you'll notice these numbers aren't arbitrary, they're all determined by differences of 2 conveniently so that the average of them is 0 and so that they're all whole numbers - you could divide them all by 2 and it wouldn't change things, it's just easier working with whole numbers)

So 1st position is "I want this person to win", 2nd position is "I like this person and if they win I'd be content", 3rd position is "I don't want this person to win" and 4th position is "I might grow a beard protesting if this person wins".

So for the same vote we have:

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

And so we have A = 3x25+(-1)x25+(-1)x25+(-1)x25 which gives A=0, B = (-1)x25+3x25+(-3)x25+(-3)x25 which gives B=(-100), C = 1x25+1x25+1x25+1x25 which gives C=100, and D = (-3)x25+(-3)x25+3x25+3x25 which gives D=0.

So we have C as the victor because they're the only person that actually has an above 50% approval rating because they have the only positive score (in fact they have a 75% approval rating) whereas no other candidate has better than a 50% approval rating, so logically C is the best choice for everyone.

Ranked-Pairs actually can be shown through Nash Equilibrium too. If you're familiar with economics enough to know what Nash Equilibrium is, then Ranked-Pairs produces a winning candidate found at the Nash Equilibrium of an election.

It doesn't mean that anyone got their FAVORITE candidate, but it does mean that all of the voters are the happiest possible with the outcome of the vote (debates on the voting system aside that is).

~Robert

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

http://i13.photobucket.com/albums/a281/hollyzuzu/6bd9dace-1d9f-469e-b069-b872b1d826dd_zpswfifvw2x.jpg

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

Mischa Brendel wrote:

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

This is why we point out that the order does matter ^_^

Re: Ranked-Pair Voting (Discussion)

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

http://i41.tinypic.com/2q2e0ig.png

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

Well, I'd say the odds are small enough. big_smile

Thanks again for explaining it all, Robert. But it is of course important to make sure that some kind of random coincidence won't have a significant impact on the outcome of the elections.

So then one question remains (which I already posed earlier): 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?



-Mischa

http://i13.photobucket.com/albums/a281/hollyzuzu/6bd9dace-1d9f-469e-b069-b872b1d826dd_zpswfifvw2x.jpg

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

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

http://i41.tinypic.com/2q2e0ig.png

Thumbs up +1 Thumbs down

Re: Ranked-Pair Voting (Discussion)

Well, you got me convinced. big_smile

And although this might have seemed like a rather pointless discussion for some (sorry!) it certainly wasn't for me. I always want to know exactly how my vote is being treated and why this is the best way of doing so. The only thing I can come up with now is that it's very important to make clear to the voters that with ranked-pairs votings that they actually look further than their favourite candidate, because the rest of their list does matter.

Thanks again for making things clear to me!



-Mischa

http://i13.photobucket.com/albums/a281/hollyzuzu/6bd9dace-1d9f-469e-b069-b872b1d826dd_zpswfifvw2x.jpg

Thumbs up +1 Thumbs down

Re: Ranked-Pair Voting (Discussion)

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

Ash

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

I think we are confusing the situation with the length examples.

There is a way to make this so a majority approve, and it is called the Instant Runoff.

Let's return to the ballot with our well mentioned candidates A through D.

There are 20 people voting, therefor 11 votes for a candidate are required for them to be elected.

Now the voter still ranks their preference through the roster but this is where it gets simple.

The votes in the first round get counted and the first round looks like this:

A: 8
B: 5
C: 4
D: 3

No clear outcome as no majority is reached whatsoever. So a second round count is done with the lowest out and those ballots for D are changed to second choice.

A: 10
B: 6
C: 5

Here A is SO Close, but needs one more vote. Unforcunately C is on the chopping block for round three... C's ballots are changed for their second preference and D's for third preference...

A: 11
B: 10

It's a close vote but in the third round of counting, A wins majority by 11.

Through this method, a winner is found not by multiple votes but a combination of eliminating the lowest person with every round of counting, but the primary choice (in this example A) keeps their first round votes/ballots. This also makes someone's vote all the more powerful and each choice has equal weight in the count, although the person making the vote still goes down their list in their head from who they feel best fits the role to the least.

Also it allows for a majority vote. We use this to elect our City Council and Mayor and I love it as it allows for everyone to have a equal shot, not just the party with the most money.

Here... it would just make the election process faster.

Here is a more in-depth explaination: https://en.wikipedia.org/wiki/Instant-runoff_voting

Last edited by Osprey (2013-07-30 19:51:30)

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

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

http://i41.tinypic.com/2q2e0ig.png

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

It might interest you to read the chart found in this scholarly journal here: http://eprints.lse.ac.uk/27685/1/Review … ERO%29.pdf

I have, for clarity, given Ranked-Pair Voting no actual personal preference in any way except in that when offered the choice between Basic Plurality and Ranked-Pair Voting - which were my only options once we had settled on the voting service: ballotbin.com which resulted in my first learning of Ranked-Pair Voting - I have opted for Ranked-Pair Voting over Basic Plurality because in the past we have examined it and concluded that it is a superior method of voting to Basic Plurality.

Instant Runoff is quite intriguing but as this comparison in the document provided has been so nicely arranged, it is of note that in this chart Ranked-Pair Voting is tied for being the most superior systems of voting and is a fair bit ahead of Instant-Runoff Voting. This is because of all the criteria given voting systems (and it's of note, none of them are "perfect" as they all have certain flaws) IRV commits what is described as a "cardinal sin" in voting, that is it does something contrary to what the voter intends - in other words the voter could cast their vote intending on what they assume to be a logical outcome yet their particular ballot actually has the reverse effect of what they had intended. Ranked-Pair Voting is one of the very few systems which does not do anything like this.

Despite the fact that IRV is in a large majority of voting systems that commit so-called 'cardinal sins of voting' and is even notably of the better systems in that group as some commit as many as 4 of these cardinal sins, it is still a most grievous accusation, no doubt, so I will do my best to explain what precisely IRV does that has caught my attention and has been explained in the article.

On your ballot you can rank candidates for IRV and I'll do so as follows:

2 Suzy
4 Winston
1 Pierre
3 Charlie
5 Jenna

In this ballot, Pierre is my first choice, I want him to win no matter what, but if Pierre is the least favorite and thus cannot win, then I want Suzy to win, and if Suzy can't win because after the first recount she's the new least favorite...you get the drift.

So the cardinal sin committed is "lack of monotonicity". So let's say Charlie ends up being the winner. All other ballots the same, in IRV it can happen that if I voted as follows:

3 Suzy
4 Winston
1 Pierre
2 Charlie
5 Jenna

That is, if I voted Charlie #2 and Suzy #3, even though I prefer Suzy to Charlie, I can actually make Suzy win by making her my 3rd choice instead of my 2nd according to my actual preferences.



Regardless of whether or not that is true, it's obvious this should never happen in voting. If I prefer Suzy to Charlie then Suzy should appear on my ballot ranked higher than Charlie. But according to this scholarly article and according to what I've now read elsewhere IRV does in fact suffer this very damaging blow to its otherwise decent reputation, and I'm inclined to believe it's true as now that this has been pointed out it's apparent that Instant-Runoff Voting actually applies an uneven distribution of weight to the voters whose ballots get recounted (uneven across those whose ballots get recounted at different stages of the vote that is).

It's a most intriguing system though, I do find it clever and interesting. Thank you for sharing this with me and with everyone, it has definitely given me some new material to think about for a while.  big_smile

~Robert

http://i41.tinypic.com/2q2e0ig.png

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

RLongtin wrote:

So the cardinal sin committed is "lack of monotonicity". So let's say Charlie ends up being the winner. All other ballots the same, in IRV it can happen that if I voted as follows:

3 Suzy
4 Winston
1 Pierre
2 Charlie
5 Jenna

That is, if I voted Charlie #2 and Suzy #3, even though I prefer Suzy to Charlie, I can actually make Suzy win by making her my 3rd choice instead of my 2nd according to my actual preferences.

~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

http://www.phoenix-rp.com/img/pips/4.png http://oi60.tinypic.com/5otabo.jpg

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

Sorry, it is. Instant-runoff voting was the language we had been using so I just stuck to it. The chart is on page 10 and it's referred to in the pdf as "Alternative Vote". It is also known as transferable vote, ranked choice voting, or preferential voting.

My example isn't intended to illustrate how that happens, it's intended to illustrate the issue that Instant-runoff voting is known to have. But yes the other ballots are missing. I'm very intrigued by this issue and will be researching precisely how this happens (purely for my own entertainment because puzzles like these are precisely what Mathematicians do for fun, lol) and then if/when I get results I'll happily share them.

Essentially what happens is the voters whose candidate is ejected in one round of voting determine which voters in the next round get their backup-opinions counted, so in a tricky way those voters' 2nd choices determine who in the 2nd round of voting gets their 3rd choices counted. Were all things fair, everyone's 2nd choice would be considered collectively (ala Ranked-Pair Voting), but it isn't.

The first group of voters to have their ballots recounted will have one of two things happen. Either their 2nd choices on their ballots determine who the winner is, or if they don't determine who the winner is then instead they determine what group of people decide the winner. This is where the problem arises, I'm just not sure mechanically what trigger makes it so that re-ordering your 2nd and 3rd choice, for example, results in a win for the person who should have otherwise logically lost between those two positions.

~Robert

http://i41.tinypic.com/2q2e0ig.png

Thumbs up Thumbs down

Re: Ranked-Pair Voting (Discussion)

Ah, I see how that happens now. Interesting.

http://www.phoenix-rp.com/img/pips/4.png http://oi60.tinypic.com/5otabo.jpg

Thumbs up Thumbs down