5 ms·

Totally with you on supoorting ranked-choice voting. It seems like a clear and obvious upgrade over what we're doing now in ways that can be mathematically veri

by gradys 7y ago

Totally with you on supoorting ranked-choice voting. It seems like a clear and obvious upgrade over what we're doing now in ways that can be mathematically verified. Question though - why prefer the Bourda Count over a Condorcet method[1] like the Schulze method[2]? I recently went down the voting method rabbit-hole when recreationally overengineering the procedure for selecting a fun offsite activity for my team. I picked the Schulze method basically because it satisfies more[3] of the formal criteria that seemed important, including the Condorcet criterion, which seems especially important. The Bourda Count method doesn't[4] seem to satisfy the Condorcet criterion, so it's possible that a candidate that would win every head to head match up would lose the election. Also, like most (all?) methods that allocate variable numbers of points to candidates, it's subject to tactical voting[5], i.e. it might be rational not to allocate any points to your second place candidate in order to maximize the margin between your first place and second place candidates, even if you prefer your second place candidate to several others. 1 - https://en.m.wikipedia.org/wiki/Condorcet_method https://en.m.wikipedia.org/wiki/Condorcet_method 2 - https://en.m.wikipedia.org/wiki/Schulze_method https://en.m.wikipedia.org/wiki/Schulze_method 3 - https://en.m.wikipedia.org/wiki/Schulze_method#Comparison_table https://en.m.wikipedia.org/wiki/Schulze_method#Comparison_ta... 4 - https://en.wikipedia.org/wiki/Borda_count#Evaluation_by_criteria https://en.wikipedia.org/wiki/Borda_count#Evaluation_by_crit... 5 - https://en.m.wikipedia.org/wiki/Borda_count#Potential_for_tactical_manipulation https://en.m.wikipedia.org/wiki/Borda_count#Potential_for_ta...

davidw 7y ago
Seems good, but perhaps a bit difficult to explain to the average voter?
- tunesmith 7y ago
  Condorcet isn't particularly hard to explain. Easier to explain than IRV anyway. Call it "Instant Round Robin" - if one candidate would beat every other candidate head-to-head, then that candidate should win. The annoying part about Condorcet enthusiasts is that they insist on lumping the uncommon "tie-breaking" methods (i.e. when there is the rare loop) in with the above general definition. That's when people start talking about Schulz, Ranked-Pairs, etc etc. I personally think a loop is valuable and shouldn't be tie-breaked - it's an indication that the voters are not ready to decide and that there should be another round of debate among the finalists before revoting. In my opinion, the main flaw with Condorcet is that it is possible to have a Condorcet Winner that does not have the "approval" of a majority of voters.
  - smeyer 7y ago
    >another round of debate among the finalists before revoting What do you do if revoting doesn't break the deadlock? Also, just in general, I think a lot of people don't want a system that involves potential revoting.
    - mjevans 7y ago
      You get the current BRexit situation, and we'll hopefully soon see some kind of historical test case the refer to...
  - flukus 7y ago
    > Call it "Instant Round Robin" - if one candidate would beat every other candidate head-to-head, then that candidate should win. And 90% of peoples eyes just glazed over, all to fix some almost entirely theoretical flaws with IRV, that's why condorcet isn't better in the real world.
    - tunesmith 7y ago
      90% of which people, the people that are enamored by "count up all first place votes, then find the person in last place, then go look at everyone's ballots and remove that person from everyone's ballots, and then count up all first place votes again, and then repeat that process until you're left with one person and then that candidate should win"?
      - flukus 7y ago
        If you're number 1 choice is knocked out you're vote goes to you're number 2 choice, if they're knocked out it goes to number 3... It's not about understanding the intricacies of how the count works but understanding what their individual vote will be doing. When it comes to what you're individual vote is doing Condorcet is much more of a black box.
jefftk 7y ago
> all? All: https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem
pwagland 7y ago
One way to think about the Borda is that it gives you the least hated candidate, instead of the most liked. From Wikipedia: The Borda count is intended to elect broadly-acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.
- eyegor 7y ago
  This seems perfect for the US, and they could even pitch it as such. Although you do start to open the game theory floodgate once you veer beyond dead simple voting systems, which could turn into a gerrymandering game if not carefully restricted.
- learnstats2 7y ago
  I don't think it works though. Unless you are careful, partisan voters will likely vote their candidate maximum and other candidates minimum - this is called bullet voting on Wikipedia. Non-partisan voters will likely vote genuinely. Since bullet voting is the dominant strategy, the election essentially reduces to First Past the Post and contains all the bad (majoritarian) incentives that FPTP does.
  - vkou 7y ago
    Most people aren't completely partisan, when given multiple palatable choices. This is less relevant in the US, with its two-party system, but is quite relevant outside of it.
    - paulgb 7y ago
      My concern is that if even a small number of people bullet vote, other people will see that their votes have less impact and adjust accordingly, in a self-perpetuating cycle.
- SamBam 7y ago
  Exactly. And (since all voting methods are flawed in some direction), the question is what do you prioritize in elections: the will of the majority, or the "acceptable" choice of even more people. Personally, I think Borda is terrible. Let's suppose the 2016 election was: Clinton, Trump, some milquetoast Republican like Jeb Bush, and someone everyone hated, bringing to total to 4. Suppose 73% of the population were fanatical Clinton fans. However, they didn't want Trump to win, so they voted Jeb #2, even though they'd much rather he didn't win. The 27% of Trump voters also listed Jeb #2. Jeb would win, in this case, even though he was a distant second choice for 73% of the population. (100 * 3 points > 73 * 4 points). Even worse would be if there were 5 or 6 candidates. Now every Clinton #1 vote is worth 6, and every Jeb #2 vote is worth 5. Jeb would win even if 83% of the voters were fanatical Clinton fans. There's no way to distinguish your second vote as "this person is also great" vs "this person is the least worst alternative." The only way to not let your far-distant second choice win is to not vote for them at all, or recruit extra candidates as shields for your preferred candidate. But then we're bringing in strategic voting and all sorts of other messiness.
drdeca 7y ago
Every “Game Form” (which is like a “Game” in the Game Theory sense, except instead of having the results be utilities for each outcome, it just has labels for the outcomes) which is “straightforward” (meaning, for each participant, what utility that participant alone assigns to each outcome label (not depending on the utilities anyone else assigns) is sufficient to determine what choices they should make to maximize their expected utility) must be either a simple vote between exactly two options (as in, everyone votes for one of the two, and an outcome label happens if it gets enough votes), or dictatorial (a single person picks an outcome), or a probability mixture of games of that form (for example, pick a random voter’s ballot, and pick whoever they picked. Or, another example, pick a random pair of candidates, and hold a vote between the two). That is to say : any deterministic voting system with more than 2 candidates, and where no voter is a dictator, is subject to tactical voting. This is Gibbard's 1978 theorem. Though, I wonder, are there game forms which are not “straightforward” but which are a Pareto improvement (in the sense of “regardless of their assignment of utilities to the possible outcomes, every voter’s expected utility is at least as high as it would in the alternate option) over game forms that are straightforward? I think probably yes? If each voter puts their utilities, and then the system computes each voter’s utility under random ballot voting, and then checks whether any probability distribution over candidates would result in a strict Pareto improvement on the expected utilities of the voters, and if there is, pucks one, and if not, defaults to the distribution from “pick a randomly selected voter’s first choice”, Well, we know that this wouldn’t be a straightforward game form, because it isn’t (equivalent to) the form required by Gibbard’s theorem, So, strategic misrepresentation of one’s (normalized vNM) utilities must be sometimes useful in it (because if it were not, then one would only need to put the same utilities each time, making it a straightforward game), but perhaps the degree of misrepresentation that could be useful would always be small enough that it would never select an option as being a Pareto improvement of the reported utilities from the random ballot method, unless it was also an actual Pareto improvement over it, using the true utility assignments? But, I’m really not sure.
- drdeca 7y ago
  Another thing that I think is relevant is the "revelation principle", which says that any "social choice function" that can be implemented by some mechanism, can be implemented by a truthful social choice mechanism. But it seems clear that the thing that I proposed as being an improvement on random ballot can't count as a mechanism which implements a "social choice function", because there can't be an equivalent mechanism which is truthful (... well, I assume that no probability mix of pairwise votes and random ballot stuff is equivalent to the thing I described. Can't see how it could be.). And I think the reason why is that the thing that I described (or, any fully specified version of it) would have to have multiple Nash equilibria. So, for it to make sense to call it a Pareto improvement, I think would need to have that _all_ of the Nash equilibria would be Pareto improvements on the thing. I am now less confident than I was that such an improvement exists.
lazzlazzlazz 7y ago
Isn't quadratic voting both simpler and less prone to tactical voting?
mjevans 7y ago
I missed your choice because I can't ever remember how to spell Schulze so I always look it up by Path Vote (my post beneath mentions both names after I found the Wikipeida article again).

by gradys 7y ago

davidw 7y ago

Seems good, but perhaps a bit difficult to explain to the average voter?

tunesmith 7y ago
Condorcet isn't particularly hard to explain. Easier to explain than IRV anyway. Call it "Instant Round Robin" - if one candidate would beat every other candidate head-to-head, then that candidate should win. The annoying part about Condorcet enthusiasts is that they insist on lumping the uncommon "tie-breaking" methods (i.e. when there is the rare loop) in with the above general definition. That's when people start talking about Schulz, Ranked-Pairs, etc etc. I personally think a loop is valuable and shouldn't be tie-breaked - it's an indication that the voters are not ready to decide and that there should be another round of debate among the finalists before revoting. In my opinion, the main flaw with Condorcet is that it is possible to have a Condorcet Winner that does not have the "approval" of a majority of voters.
- smeyer 7y ago
  >another round of debate among the finalists before revoting What do you do if revoting doesn't break the deadlock? Also, just in general, I think a lot of people don't want a system that involves potential revoting.
  - mjevans 7y ago
    You get the current BRexit situation, and we'll hopefully soon see some kind of historical test case the refer to...
- flukus 7y ago
  > Call it "Instant Round Robin" - if one candidate would beat every other candidate head-to-head, then that candidate should win. And 90% of peoples eyes just glazed over, all to fix some almost entirely theoretical flaws with IRV, that's why condorcet isn't better in the real world.
  - tunesmith 7y ago
    90% of which people, the people that are enamored by "count up all first place votes, then find the person in last place, then go look at everyone's ballots and remove that person from everyone's ballots, and then count up all first place votes again, and then repeat that process until you're left with one person and then that candidate should win"?
    - flukus 7y ago
      If you're number 1 choice is knocked out you're vote goes to you're number 2 choice, if they're knocked out it goes to number 3... It's not about understanding the intricacies of how the count works but understanding what their individual vote will be doing. When it comes to what you're individual vote is doing Condorcet is much more of a black box.

jefftk 7y ago

> all? All: https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem https://en.wikipedia.org/wiki/Gibbard–Satterthwaite_theorem

pwagland 7y ago

One way to think about the Borda is that it gives you the least hated candidate, instead of the most liked. From Wikipedia: The Borda count is intended to elect broadly-acceptable options or candidates, rather than those preferred by a majority, and so is often described as a consensus-based voting system rather than a majoritarian one.

eyegor 7y ago
This seems perfect for the US, and they could even pitch it as such. Although you do start to open the game theory floodgate once you veer beyond dead simple voting systems, which could turn into a gerrymandering game if not carefully restricted.
learnstats2 7y ago
I don't think it works though. Unless you are careful, partisan voters will likely vote their candidate maximum and other candidates minimum - this is called bullet voting on Wikipedia. Non-partisan voters will likely vote genuinely. Since bullet voting is the dominant strategy, the election essentially reduces to First Past the Post and contains all the bad (majoritarian) incentives that FPTP does.
- vkou 7y ago
  Most people aren't completely partisan, when given multiple palatable choices. This is less relevant in the US, with its two-party system, but is quite relevant outside of it.
  - paulgb 7y ago
    My concern is that if even a small number of people bullet vote, other people will see that their votes have less impact and adjust accordingly, in a self-perpetuating cycle.
SamBam 7y ago
Exactly. And (since all voting methods are flawed in some direction), the question is what do you prioritize in elections: the will of the majority, or the "acceptable" choice of even more people. Personally, I think Borda is terrible. Let's suppose the 2016 election was: Clinton, Trump, some milquetoast Republican like Jeb Bush, and someone everyone hated, bringing to total to 4. Suppose 73% of the population were fanatical Clinton fans. However, they didn't want Trump to win, so they voted Jeb #2, even though they'd much rather he didn't win. The 27% of Trump voters also listed Jeb #2. Jeb would win, in this case, even though he was a distant second choice for 73% of the population. (100 * 3 points > 73 * 4 points). Even worse would be if there were 5 or 6 candidates. Now every Clinton #1 vote is worth 6, and every Jeb #2 vote is worth 5. Jeb would win even if 83% of the voters were fanatical Clinton fans. There's no way to distinguish your second vote as "this person is also great" vs "this person is the least worst alternative." The only way to not let your far-distant second choice win is to not vote for them at all, or recruit extra candidates as shields for your preferred candidate. But then we're bringing in strategic voting and all sorts of other messiness.

drdeca 7y ago

Every “Game Form” (which is like a “Game” in the Game Theory sense, except instead of having the results be utilities for each outcome, it just has labels for the outcomes) which is “straightforward” (meaning, for each participant, what utility that participant alone assigns to each outcome label (not depending on the utilities anyone else assigns) is sufficient to determine what choices they should make to maximize their expected utility) must be either a simple vote between exactly two options (as in, everyone votes for one of the two, and an outcome label happens if it gets enough votes), or dictatorial (a single person picks an outcome), or a probability mixture of games of that form (for example, pick a random voter’s ballot, and pick whoever they picked. Or, another example, pick a random pair of candidates, and hold a vote between the two). That is to say : any deterministic voting system with more than 2 candidates, and where no voter is a dictator, is subject to tactical voting. This is Gibbard's 1978 theorem. Though, I wonder, are there game forms which are not “straightforward” but which are a Pareto improvement (in the sense of “regardless of their assignment of utilities to the possible outcomes, every voter’s expected utility is at least as high as it would in the alternate option) over game forms that are straightforward? I think probably yes? If each voter puts their utilities, and then the system computes each voter’s utility under random ballot voting, and then checks whether any probability distribution over candidates would result in a strict Pareto improvement on the expected utilities of the voters, and if there is, pucks one, and if not, defaults to the distribution from “pick a randomly selected voter’s first choice”, Well, we know that this wouldn’t be a straightforward game form, because it isn’t (equivalent to) the form required by Gibbard’s theorem, So, strategic misrepresentation of one’s (normalized vNM) utilities must be sometimes useful in it (because if it were not, then one would only need to put the same utilities each time, making it a straightforward game), but perhaps the degree of misrepresentation that could be useful would always be small enough that it would never select an option as being a Pareto improvement of the reported utilities from the random ballot method, unless it was also an actual Pareto improvement over it, using the true utility assignments? But, I’m really not sure.

drdeca 7y ago
Another thing that I think is relevant is the "revelation principle", which says that any "social choice function" that can be implemented by some mechanism, can be implemented by a truthful social choice mechanism. But it seems clear that the thing that I proposed as being an improvement on random ballot can't count as a mechanism which implements a "social choice function", because there can't be an equivalent mechanism which is truthful (... well, I assume that no probability mix of pairwise votes and random ballot stuff is equivalent to the thing I described. Can't see how it could be.). And I think the reason why is that the thing that I described (or, any fully specified version of it) would have to have multiple Nash equilibria. So, for it to make sense to call it a Pareto improvement, I think would need to have that _all_ of the Nash equilibria would be Pareto improvements on the thing. I am now less confident than I was that such an improvement exists.

lazzlazzlazz 7y ago

Isn't quadratic voting both simpler and less prone to tactical voting?

mjevans 7y ago

I missed your choice because I can't ever remember how to spell Schulze so I always look it up by Path Vote (my post beneath mentions both names after I found the Wikipeida article again).