Posts made by marcosb

@Keith-Edmonds Thanks! Unfortunately it doesn't send me any form of notification, will respond.

@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):

I strongly disagree with your interpretation of the game theory here. If the 51% knew they were going to be 51% then sure but they do not.

But they will after the election results - and when they see the election results showing that 51% of them gave CandidateR the highest score, the cardinal system will be vetoed in an instant - that, or everyone will switch to bullet voting so it never happens again.

The beauty of IRV Prime is that'll never happen - like you said, they don't KNOW that they have 51%, but they'll hope they do; so they'll rank #1 their favorite but #4 a safe compromise.

If it turns out that they really did have 51%, they'll win & it'll be a vote of confidence for the voting system.

On the other hand (as will frequently happen) if they only have 48% & the center has the remaining 3% & the center candidate wins, they'll see very clearly in the results why center won.

in any given election they could be the 49%. What people want is a system where independent of which side they are on they will get a good winner. This is a concept put forth by John Rawls called "the Veil of Ignorance".

I don't think people want a good winner - people are selfish, they want the winner that best represents them.

Nothing will piss off a democracy more than a majority candidate losing (in spite the fact that a more representative candidate would actually be better for the country).

Each individual voter, in general, cares about themselves, not the general good.

No but I think this is still a polarizing system relative to neutral. Score is balance and Approval is antipolarizing or centerist.

IRV-Prime is a forceful unpolarizing system - as long as a polar side doesn't have the majority (which is almost certain most of the time), it pushes voters towards a compromise.

Approval & score would be the best if people voted "for the greater good" & weren't so easily manipulated by campaign ads.

But do we want the system that works best with humans (selfish & easily swayed)? Or the system that works best in a utopian society?

@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):

It depends on who you ask. In this situation

49 = L:5, CR:4
51 = R:5, CR:4

Lets say this was the 2016 presidential race and R=Trump while L=Hillary. A system that could find the CR candidate would have been better.

Better for the country, agreed; but look at the state things are in now, does it seem like people care what's better for the country?

That 51 majority would be pissed & immediately vote to outlaw the voting system; the question is: how can we get those 51 people to think "oh yeah it's clear CR is the winner & we lost" (ok, you'll never get that with all 51; you'll always have the sore losers)

I think IRV Prime might be that, because that center sucks away that majority - i.e. I think in practice, it will get the results you expect while at the same time getting everyone supportive of the voting system instead of against it.

Many people would see that immediately. Furthermore, you would only get such candidates in such a system. People often assume that you get the same candidates when you have different systems but this is false. Unviable candidates do not even show up.

Completely agree - I think that's actually the beauty of IRV Prime, it'll change the parties. Do you believe the major parties would continue to be polarizing when they see that's a losing strategy in the general election? I highly doubt it.

This is a good example since there will always be a few voters of all orderings. I would make this point on your electowiki page.

Will do.

In summary, you have made a better IRV at the cost of some complexity. I do not study ranking systems for reasons that should be clear by now so I cannot speak with any authority on how it compares to other ranking systems. IRV is likely one of the worst so I would not celebrate yet. Also, I would not make the bold claims about strategy or monotonicity without talking to a proper expert on such systems.

Completely agreed - I've been reaching out but have been having a tough time finding the right folks! I think I may have finally gotten in contact with some so we'll see where it goes.

Thanks so much for the views/thoughts, very much appreciated!

So your example actually perfectly demonstrates why it gets the bad name of "dictatorship mechanism"; you had this example:

49 = L> CR > R
51 = R > CR > L

So your thought is that CR, with wider support, should get elected; but in STAR/IRV/IRV-Prime, R (majority) gets elected

However, if we had this:

49 = L> CR > R
49 = R > CR > L
2 = CR > L > R

Then in fact CR does win (with IRV-Prime), even though only 2 voters ranked them as #1; these 2 voters seem like dictators, as far more voters ranked L as #1 & R as #1

@Keith-Edmonds said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):

later-no-harm is the opposite of that. It is that no matter what you never need to compromise.

It does not necessarily mean that; it simply means that your ranking order is never disregarded. The problem is that if ranking order is disregarded, then it could motivate people to not rank & then you're back to square 1

The key here is: in a democracy, if you are part of the majority, then maybe you don't need to compromise; it's shitty but it's just a side-effect of democracy

But the key is: how often does that happen in practice, that you are part of the majority? You can see that in practice it flip-flops, like a pendulum from left-to-right, precisely because there is rarely a majority candidate

So we should try to address the practical case (i.e. taking advantage of that middle) & giving the best results by taking advantage of what people think they want

The fact that there is such a thing as a "spoiler candidate" I think is clear proof that a majority is easy to destroy.

Does the compromise candidate win in this situation when you use IRV-prime?

49 = L:5, CR:4
51 = R:5, CR:4

Because IRV-Prime fulfills condorcet & thus majority winner, a majority winner will always win; but then, as I mentioned, how often does this happen in practice? Look at the 1856 & 1860 elections: when there are > 3 viable candidates, no candidate gets a majority.

Or in ranking

49 = L> CR > R
51 = R > CR > L

CR should win under this situation given an ethos of Utilitarianism. I think IRV-Prime does find a good balance for a ranking system. However, ranks cannot tell between the first scoring and this

49 = L:5, CR:1
51 = R:5, CR:1

where R is the Utilitarian winner.

They "can't tell the difference" because the majority candidate wins (what I mean is, if a ranking system "not telling the difference" was electing CR in both cases, that'd be really terrible; but it ends up electing R in both cases)

Though I agree that in the first scenario CR is more representative, I have to come back around to real-world practical: how likely would this be? That R would have a majority? I think it's almost certain that in practice there are centered people & they'd take a big enough chunk such that R does not have the majority, and then IRV-Prime would select the compromise candidate.

More importantly, the will of the voters (even if shitty) does have to be respected; it's like the king in the little prince; if people saw a result like this, they'd immediately want to eliminate the voting system because they'd feel short-changed when a majority winner loses.

Now, we can agree that's shitty - but it is also reality.

Yes, but you are assuming that such effects will have a net push toward bullet voting. I think it will be the opposite. Real world approval voting examples give evidence to that.

We just don't know - approval voting has never been used in a major election where campaigns would put significant funds into saying "bullet vote or I might lose."

What we do know is that campaigns are self-serving; if they think anything will give them an edge (which bullet voting would), if that incentive is there, they'll take it.

I am not sure that is correct. I need to double check

The best demonstration of this I could find (which made it really clear but took some thinking) is the informal proof of Arrow's impossibility theorem

I have never viewed this as a good thing. It is equivalent to never making a compromise or consensus

I don't disagree with you that people being unwilling to compromise is a bad thing (my goal, as you've seen, is to give people no choice but to compromise)

It ends up being counter-intuitive; effectively what IRV-Prime is getting people to do is: "look, be uncompromising, stick to your guns; but there's nothing to lose by setting up your priorities as #1 uncompromising 100% of what I want & #2 if #1 is impossible, compromise & get 50%"

It's giving in to people's needs while at the same time using the sum of the parts to an advantage (that as a population, we fall somewhere in the middle)

There have been studies showing people do not bullet vote

I don't think those studies take into account the macro, i.e. what happens at large scale when large-scale targeted campaign ads kick in; a system must be immune to that

Dictatorship implies it is non-democratic. This is bad

The name is horrible, perhaps why people have strayed away from it . It is not at all implying undemocratic; rather, it's saying that in a perfect all-way tie, a single voter chooses any winner they want; in plurality, this is straightforward: if there's 5000 voting for L & 5000 voting for R, then I alone get to choose who wins

With ranked, it's a little more complicated; but you can still imagine a scenario where it does (reworking the example I posted on electowiki):

Right voters (R > CR > L) N
Pivotal Voter (?) 1
Left voters (L > R > CR) N

(It's a little strange here that L voters prefer R over CR; perhaps in practice we don't ever get such a perfect cycle, but just to communicate the idea)

So the pivotal voter here is considered the dictator; whatever they choose as #1 (CR, R, L; doesn't matter), wins - that's true in IRV Prime

You can see that they're a "dictator" because they are a single voter whose choice is all that matters; but they're only in that position because their choice becomes the majority (so it's democratic)

In the plurality vote, the 5001th voter to vote for L & beat out R's 5000 would also be considered the dictator; had he chosen R, R would win; but it's a poor choice of terms, they're really the decider; their choice only matter because they're in the majority

Trying to understand Arrow's impossibility theorem (the informal proof, part 2)

It says that with Profile K we have:

B > C > A: k -1
A > B > C: 1
A > B > C: N - k - 1

(Here, A wins, as expected, in IRV as well as IRV-Prime)

And with Profile N:

C > B > A: k -1
B > A > C: 1
A > C > B: N - k - 1

In IRV, A wins. In IRV-Prime, B wins.

So I think by this definition:

dictatorship is the only ranked voting electoral system that satisfies unrestricted domain, Pareto efficiency, and independence of irrelevant alternatives. Similarly, by Gibbard's theorem, when there are at least three alternatives, dictatorship is the only strategyproof rule.

So I think the key here is that IRV-Prime simply satisfies the dictatorship mechanism, which is why it's strategyproof, i.e. voter k chooses the winning candidate by whatever they rank as #1

But later-no-harm is also satisfied.

So the question is: why do people believe that Arrow's impossibility theorem & Gibbard–Satterthwaite theorem imply a voting method cannot satisfy later-no-harm + Monotonicity criterion + Condorcet criterion?

That's not at all correct in the case of a method which has a dictatorship mechanism

Later-no-harm is the main reason; my main worry is that if major parties feel that ranking a candidate after them will ruin their chances of winning, they'll encourage their supporters/voters to bullet-vote, which will degrade to ~plurality (a single max-point vote for the favorite & no one else ranked)

Let's look at the flip-side, though (just theoretically): suppose that IRV-Prime does satisfy the monotonicity criterion as well as later-no-harm (I realize that seems to break every rule but let's go with it)

What would be the reason not to go with it (besides possibly that the counting is too complex?)

Wouldn't its benefits (i.e. having major parties actually encourage voters to rank others, actually giving 3rd parties a chance, as well as monotonicity) outweigh that detriment?

I.e. isn't it worthwhile trying to see if if it at least does satisfy these criteria like it seems to?

@Keith said in IRV-Prime (meeting later-no-harm & Condorcet criterion; possibly immune to dishonest strategy?):

Right. I missed that. This is a huge advantage over IRV. If you are going to point out that STAR also gets the same winner as IRV you have to give an interpretation of the translation of ranks to scores. A reasonable interpretation is

47 = L:5, CR:4
39 = R:5, CR:4
5 = R:5
5 = CR:5, R:4

in which case CR wins (or my math is bad). In any case I see the argument you are trying to make. Consider

49 = L:5, CR:4
51 = R:5, CR:4

where R wins and the clear best winner is CR.

Exactly; I'll expand on why STAR also fails because CR is eliminated before the runoff (similar issue as IRV)

This is why I invented STLR.

Very interesting, let me take a look & understand it first before replying.

I am no expert on these proofs but Gibbard-Satterthwaite theorem would forbid this. Making such a claim will require a proof.

Arrow's impossibility theorem would also forbid this. Passing it in a situation then IRV fails does not prove monotonicity. You are likely just shifting the failures to another spot. If this does pass either of these criteria that would make you very famous very quick. I am quite skeptical. My suggestion is for you to look into proofs.

Agreed; passing a situation that IRV fails means nothing (I mean, it could be an indication; but it's not enough) & a proof is necessary. I think I've found what's wrong with Gibbard-Satterthwaite theorem, but I'm not sure how to put it in a proof.

In essence, the crux of it is that it assumes the method picks the wrong winner; effectively, it says "given a system which eliminates Paper & then has Scissors run against Rock" - the problem is, why is this assumption being made? Why would we eliminate Paper first if we know Scissors voters prefer Paper over Rock?

If the system picks the candidate with the most support via elimination (which IRV-Prime does) while at the same time only transferring your votes to your next preferred candidate if your candidate can't win, then by definition tactical voting does no good.

Woops missed your comment about Monotonicity criterion: I think (& would appreciate your help) that it is met by IRV-prime, too

Looking at the example here:
https://en.wikipedia.org/wiki/Monotonicity_criterion#Instant-runoff_voting_and_the_two-round_system_are_not_monotonic

That's almost exactly the example I have for IRV-prime

In IRV-prime, Center would be in the schwartz set; we would find the classic IRV winner (L):

Round n-1:
L: 35
R: 33
C 32

Round N:
L: 51
R: 48

Now we take L ("Winners" set) & run against others in Scwhartz set (of which C is one):
Round Prime-N (Step 3 in IRV-Prime) for C
C 32 + 28 <-- we take the top 1 & put in winners-prime
L: 35 + 5

We run the final round with candidates in Winners set & Winners-Prime set:

C 60
L: 40

And in fact C wins in IRV Prime (so it does seem to satisfy monotonicity, so you may actually be interested)

i.e. in IRV Prime, no votes can be changed to make L or R win, except to rank L/R above C (i.e. get more voters who prefer L or R over C)

"Least polarizing candidate (in the Schwartz set)": I had hoped that my example on the page would clarify this (the example is supposed to signify R=Right, L=Left, CR=Center-right)
The idea here is: if a party chooses the most polarizing candidate in a primary (the one that is uncompromising; parties tend to choose the most party-ish candidate), then they will almost certainly lose in the general election; voters (due to later-no-harm satisfied by the method) have every reason to rank something like this:

1-3) Favorite candidates
4) Favorite frontrunner
5) Least-hated who is a frontrunner with opposing views

Which is likely to leave the polarizing frontrunners with insufficient votes (i.e. a non-majority) & a more center/compromising candidate to win the majority

"Find the instant runoff winnerS": yes apologies I tried to generalize to include multi-winner STV; for a single winner IRV, NumWinners=1

"Dishonest strategy": I think the best definition here would be "voting counter to what I want (lying) to get something I want" - a great example would be to rank a non-favorite higher to eliminate a frontrunner so that your favorite can win - IRV prime is immune to it because the only way a candidate can win is by having a larger majority

"Seems like a patch": In a sense, this is true; but the results of that patch (i.e. being a system that seems to defy Gibbard and Statherwaite) make it at least, academically, worthy of a look - the key being that it's not so much of a patch as it is a fix for IRV's primary failure: that winning candidates are disqualified early by candidates that are guaranteed to lose

A great way to look at this is an alternative perspective on rock-paper-scissors; at first glance, it seems like a deadlock, like each has an advantage over the other & it's a loop; but that's not really true, if you rephrase the question: suppose it's instead phrased this way:

Suppose there's a group of voters who like Paper & Scissors; some are P > S, some are S > P
Now suppose that group of voters were to go against Rock; which candidate should they stand behind?

That's really what this voting method aims to solve (& why it has such interesting properties)

I seem to have proposed a method (I may not be the first; happy to give credit if I'm not) that may meet LNH as well as Condorcet criterion, as well as possibly being immune to dishonest strategy (all which is generally accepted as impossible via Gibbard and Statherwaite)

Would appreciate it if some experts could look it over (it's somewhat straight-forward to understand & the likelihood is that I'm just missing something; but, at least academically, if the proof is correct, seems worthy of a look)
https://electowiki.org/wiki/IRV_Prime