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  #41  
Unread 03-06-2019, 08:48 AM
Matt Q Matt Q is offline
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Hi Max,

As I understand it, the paradoxical result is the same as failing to produce a winner. I'm assuming that the electoral method being used produces a ranking consistent with majority choices, and that this ranking is the outcome of the election: it decides who is first, second, third place etc. In the problematic case (assuming three candidates) this method cannot produce a ranking because:

most people prefer A over B, and
most people prefer B over C, and
most people prefer C over A,

So, the ranking consistent with majority choices is paradoxical, or alternatively, it is impossible to rank the candidates, even though each individual voter has produced a logical ranking on their ballot sheet. Consequently, you do not have a winner.

A cannot be the winner, because more people prefer C to A.
B cannot be the winner because more people prefer A to B; and
C cannot be the winner because more people prefer B to C.

The method fails to rank the candidates and hence produces a non-result, and hence, no winner.

"A Condorcet method is an election method that elects the candidate that would win a majority of the vote in all of the head-to-head elections against each of the other candidates, whenever there is such a candidate. A candidate with this property is called the Condorcet winner. [...] A Condorcet winner does not always exist in every election because the preference of a group of voters selecting from more than two options can be cyclic—that is, for each candidate it might be possible to select an opponent where the opponent would win a majority of the votes." from here, my emphasis

Not producing a winner is a problem when one of the requirements of the method is that it does produce a winner, e.g. when electing a president.

This outcome: not producing a winner, is most definitely much more likely with this particular ranking method than with a single-vote, first-past-the-post method. With the latter method, the odds of a tie for first place is vanishingly small in a nationwide vote.

This, if nothing else, is a practical concern when choosing a method.

So I disagree that not finding a winner is just as likely with a first-past-the-post system. And I disagree that producing a cyclic/paradoxical ranking is just as likely with a one-vote-per-person system: as far as I can see, it's impossible to produce a cyclic/paradoxical ranking in this way -- the worst case scenario is that you get a tie.

If, on the other hand, we're using a different kind of ranking or PR method, then the outcomes will be different.

best,

Matt

Last edited by Matt Q; 03-06-2019 at 10:11 AM.
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  #42  
Unread 03-06-2019, 10:43 AM
Max Goodman Max Goodman is offline
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Thanks for explaining that to me, Matt.

Quote:
Originally Posted by Matt Q View Post
As I understand it, the paradoxical result is the same as failing to produce a winner.
If that's the definition of failing to produce a [deserving] winner, then, when voters have paradoxical preferences, no system can produce one; the voters' preferences make it impossible. This isn't a weakness of ranked choice unless we agree that concealing paradoxical preferences is a strength. (I see pros and cons.)

[We may have to agree to disagree about whether paradoxical preferences exist equally whether or not the voting system allows them to be expressed. On that issue, we're writing in circles.]

Quote:
Originally Posted by Matt Q View Post
"A Condorcet method is an election method that elects the candidate that would win a majority of the vote in all of the head-to-head elections..."
Then a Condorcet method is a specific type of ranked-choice voting. Thanks for teaching me a new term. Such a method likely has some benefits. It has the weakness you point out.

There are simpler ranked-choice methods that don't share the weakness. In them, lower-tier candidates are eliminated and their votes given to their voters' preferences among the remaining candidates.

Last edited by Max Goodman; 03-06-2019 at 10:45 AM.
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  #43  
Unread 03-06-2019, 11:57 AM
R. S. Gwynn's Avatar
R. S. Gwynn R. S. Gwynn is offline
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Bernie is an independent. If he wins the nomination in the primaries, party loyalists may feel that he's been forced upon them and be less enthusiastic about his campaign.

Biden is a party loyalist. The party will stand behind him, but his mouth has a way of getting him into trouble.

They are 77 and 76, respectively.

So far, no other Democrat candidate has shown much mass appeal.
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  #44  
Unread 03-06-2019, 02:42 PM
Matt Q Matt Q is offline
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Hi Max,

Quote:
Originally Posted by Max Goodman View Post
If that's the definition of failing to produce a [deserving] winner, then, when voters have paradoxical preferences, no system can produce one; the voters' preferences make it impossible. This isn't a weakness of ranked choice unless we agree that concealing paradoxical preferences is a strength. (I see pros and cons.)
I guess there are a number of criteria by which a method of electing a president can be judged. One of them, for very practical reasons, would be that the method ultimately generates a winner. For that reason, a method which may not produce a winner, such as the Condorcet method, has a weakness: There's a risk that either you end up with no president, or worse, you're stuck with Trump indefinitely! So, I'd say if we want to guarantee electing a president, then this is a weakness of the Condorcet model. I think we're agreed on that.

The definition of failing to produce a winner I'm using is simply that the system fails to produce a winner. The ballot is taken, the votes are processed, the method is applied, and the person announcing the winner stands up and says, "Sorry folks, we don't have a winner". "Deserving" wasn't related to the point I was making.

But yes, if we define a deserving winner as a Condorcet winner, and there is actually no Condorcet winner (due to paradoxical averaged population preferences), then clearly no other method will find a Condorcet winner, because one doesn't simply exist. I agree with you on this.

Quote:
[We may have to agree to disagree about whether paradoxical preferences exist equally whether or not the voting system allows them to be expressed. On that issue, we're writing in circles.]
I think we also agree on this: if paradoxical preferences exist in the population, they exist irrespective of whether or not the chosen voting method is capable of measuring them. They will only show up under some methods, and not under others, but they'll still be there. If that's your point I also agree.

However that's different from saying:

Quote:
A paradoxical result (posts 36 and 37) is not the same as failure to produce a winner (39), and neither of those outcomes is any more likely under ranked choice than under a vote-only-for-your-favorite-candidate system. (A paradoxical result may feel more likely under ranked choice, but only because that system can reveal a paradox that would otherwise have remained hidden. Ranked choice may therefore be more interesting to those intrigued by paradoxes and probability, but that's not a weakness.)
You can only get a paradoxical result if you use a particular method, like the Condorcet method, that's capable of generating such a result. You literally can't get a paradoxical result if you use a vote-only-for-your-favorite-candidate system. It's not one of the possible outcomes of applying that system. So getting a paradoxical result is more likely under the Condorcet method, since it's impossible to get one under the vote-only-for-your-favorite-candidate system. However, not getting a paradoxical result doesn't mean that population doesn't have paradoxical average preferences. It just means that the vote-only-for-your-favorite-candidate system won't register these, because it's not measuring ranked preferences on the ballot paper. I think we're agreed on this too.

So, hopefully we're not disagreeing about anything, but I apologise if I'm missing your point again!

best,

Matt
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  #45  
Unread 03-06-2019, 02:52 PM
Max Goodman Max Goodman is offline
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Hi, Matt,

Are we agreed that not every ranked-choice method is a Condorcet method?
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  #46  
Unread 03-06-2019, 03:08 PM
Matt Q Matt Q is offline
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Max,

There are certainly many ways to use preference-ranked balloting that will still produce a winner if no Condorcet winner exists. Is that what you're asking?

Did we agree on all the other stuff?

Matt

Last edited by Matt Q; 03-06-2019 at 03:17 PM.
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  #47  
Unread 03-06-2019, 03:16 PM
Max Goodman Max Goodman is offline
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Yes, Matt. I think we were talking at cross-purposes, not understanding each other's terms.

Cheers.
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  #48  
Unread 03-07-2019, 03:33 AM
Erik Olson Erik Olson is offline
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Quote:
Originally Posted by R. S. Gwynn View Post
Bernie is an independent.
We call the politician who runs for office not affiliated with the Republican nor with the Democratic Party the independent on the ticket. In contrast, Bernie Sanders Signs Democratic Party Loyalty Pledge For 2020 Run. This officially affirms to the Democratic National Committee the following: that they are a Democrat, a member of the Democratic Party; that they will accept the Democratic nomination; and will run and will serve as a member of the Democratic Party.
Quote:
Originally Posted by R. S. Gwynn View Post
If he wins the nomination in the primaries, party loyalists may feel that he's been forced upon them and be less enthusiastic about his campaign. Biden is a party loyalist. The party will stand behind him, but his mouth has a way of getting him into trouble.
Observation:
As with advantage, so too with baggage, each brings his own. None run for president without liabilities unique to them, whether Warren haunted by the baggage of an ancestry fiasco or Biden by the specter of a plagiarism scandal, whether Beto open to the charge of legislative inexperience to his name or Sanders to that of an impolitic past with his party. We can pin something to damper the promise of you name it easily enough; after all dirty laundry aired, however, it is very difficult to tell the proportion of susceptibility between the runners, let alone which Achille's heel will prejudice the greater part of the voting public come election day. All the more reason why I, for my own part, will choose whomever I think best qualified. By that calculation, not letting fears of this or that contingency predicted of the multitude, fickle and unreliable, deter my choice. I do not disagree; both have to watch out. True.

Cheers,
Erik

Last edited by Erik Olson; 03-07-2019 at 03:08 PM.
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