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Voting is a Sham Mathematically Speaking

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Re: Voting is a Sham Mathematically Speaking

#41

Post by bad_user »

diego wrote: post #26
maratd wrote: post #25

This is off. Voting is not a system for selecting the best candidate. Voting, in whatever forms it exists, is a system to avoid violence and conflict. Each side feels it had a fair shot, regardless of outcome. The purpose of voting is to leave you with that feeling, to avoid unpleasant behavior from the losing party. The best person for the job almost never gets it. That's why we don't vote people in when hiring some…

Yes, and in addition it's also a system to ensure that elected officials and their parties have accountability. If you win an election and then "betray" your voters, you won't be reelected. If you can't be reelected, you could damage the chances of your party. In essence, democracy in its current form is not so much about choosing the right/best candidate. It's more about making sure the winner cannot become a despot…

In addition, people do not even try voting for the best candidate. People usually vote for the candidate whose interests best align with their own interests and if we're talking about that, then we can't avoid talking about compromises.

Which is why it's easy to see why preferences between candidates may be non-transitive, as the space we're talking about is no longer one-dimensional so candidates don't have a natural order.

Re: Voting is a Sham Mathematically Speaking

#42

Post by im3w1l »

kscaldef wrote: post #29
Noughmad wrote: post #14

I find it interesting that in all those discussions about voting systems, which are mostly focused on USA president elections, nobody mentions two-round voting, also known as run-off voting. This is what we have in Slovenia for electing our president. In the first round, there are many candidates, and each voter can vote for one. If any candidate gets at least 50% of votes, he automatically wins. If, on the other han…

I don't believe this satisfies the Condercet criterion either. Consider these rankings of preferences: 20% A ... 20% B ... 15% C ... 15% D C ... 15% E C ... 15% F C ... In a two-round run-off, one of A or B will be elected, despite the fact that 60% of voters prefer C over either A or B.

And in the real world, people would second guess this, and enough people would tactic vote for C that it would't be a problem.

"But then they can't vote for their prefered candidate which was the whole point"

Well, some people can. D, E, F could still get a few percentage points. More importantly, I don't think we would see convergence to a 2-party system.

Unless I am missing something, it looks like at least 3 parties could be sustained.

Re: Voting is a Sham Mathematically Speaking

#43

Post by saraid216 »

bo1024 wrote: post #16
saraid216 wrote: post #5

> Voting is a method that a group of people use to pick the “best choice” out of a set of candidates. It’s pretty obvious, right? And like many other pieces of "common sense", this isn't correct. Wikipedia says, "Voting is a method for a group such as a meeting or an electorate to make a decision or express an opinion—often following discussions, debates, or election campaigns. Democracies elect holders of high offic…

> Wikipedia says, "Voting is a method for a group such as a meeting or an electorate to make a decision or express an opinion—often following discussions, debates, or election campaigns. Democracies elect holders of high office by voting." This is very different from "picking the best choice". I don't see how they are different. The author never said that candidates have to be people. Substitute the word "alternative…

> I don't see how they are different.

"I think this is the way we should proceed" is qualitatively different from "I think this is the best choice".

> The author never said that candidates have to be people. Substitute the word "alternatives" if you prefer.

Substitute it in place of what? Where did I require that the candidates must be people?

Re: Voting is a Sham Mathematically Speaking

#44

Post by saraid216 »

derleth wrote: post #22
saraid216 wrote: post #17

Earlier quoted context omitted.

Tell that to the next person who complains that their vote doesn't count.

It's entirely possible to be active in the ACLU, for example, and still be annoyed that since you live in Montana your vote for a Democratic presidential candidate is basically pointless.

Pointless for what purpose?

Re: Voting is a Sham Mathematically Speaking

#45

Post by saraid216 »

anigbrowl wrote: post #32
maratd wrote: post #25

This is off. Voting is not a system for selecting the best candidate. Voting, in whatever forms it exists, is a system to avoid violence and conflict. Each side feels it had a fair shot, regardless of outcome. The purpose of voting is to leave you with that feeling, to avoid unpleasant behavior from the losing party. The best person for the job almost never gets it. That's why we don't vote people in when hiring some…

Voting, in whatever forms it exists, is a system to avoid violence and conflict. If only someone had explained this to your namesake :-) http://en.wikipedia.org/wiki/Jean-Paul_Marat

Not really. Voting only avoids violence and conflict when the possible combatants may actually participate in the vote.

Re: Voting is a Sham Mathematically Speaking

#46

Post by Empact »

gus_massa wrote: post #36
DennisP wrote: post #4

Earlier quoted context omitted.

Plus it doesn't run into trouble with Arrow's theorem, since it's not a "rank-order voting system," unlike plurality, instant runoff, and various others. Range voting has the same advantage. In computer simulations measuring how well the election result matches voter preferences, either range or approval is as much an improvement over plurality as plurality is over picking someone at random (or, if you like, monarchy…

I'm not sure about the definitions, but if the Arrow theorem doesn't apply to the Approval Voting sistem them I think that it must not be applicable to the "majority rules" criterion. In this two system the idea is that you get very little information from the voters (best candidate / a set of candidates) and don't know all the information about the order of preference and the relative strength. So I don't understand…

> I don't understand why having less information is better (theoreticaly).

A ranked-choice ballot only encodes the orders the candidates against one another, whereas approval and score votes also encode the candidates' positions within the voter's range of subjective preferences. That is, if we have 3 candidates (A, B, C) and a few voters which each voters has a range from love to hate for each candidate, like so:

  Love                       Hate
   |-A--B-------------------C-|
   |-A-------------B-----C----|
   |-------------------A-B-C--|
   |-A-B---C------------------|
Under ranked choice voting, every one of these voters' ballots would look the same:

   1)A, 2)B, 3)C
Ranked choice voting encodes the ordering of the preferences, but the intensity of those preferences is lost when the ballot is cast. Whereas under approval and score voting, every one of these voters represents their preferences differently, because they're reflecting their personal response to each candidate:

     Approval | Disapproval
   |-A--B-----|-------------C-|
   |-A--------|----B-----C----|
   |----------|--------A-B-C--|
   |-A-B---C--|---------------|
Of course, some information is lost in the fact that we only have 2 values approval/disapproval to encode positional preferences. But I would argue this information is already more meaningful than a fully-expressed ranked ballot. And if necessary, score voting can capture more of that information by offering > 2 levels to divide the candidates into.

Re: Voting is a Sham Mathematically Speaking

#47

Post by jsharpe »

gabemart wrote: post #37

I found this article quite frustrating. >Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman. I found this by far the most interesting assertion, but the examples under…

I am wondering that too. He also gave the example of Ford beating Reagan (in the Republican primary), Carter beating Ford in the general election in 1976, and then Reagan beating Carter in 1980, but this is also not a great example since the Republican primary group is very different than the general electorate.

Re: Voting is a Sham Mathematically Speaking

#48

Post by Dove »

gabemart wrote: post #37

I found this article quite frustrating. >Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman. I found this by far the most interesting assertion, but the examples under…

Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)?

Sure, that's easy to construct.

    Peter's preferences: A, B, C
    Paul's: B, C, A
    Mary's: C, A, B
The group prefers A over B, by a 2-1 vote. Likewise B over C, and C over A.

Re: Voting is a Sham Mathematically Speaking

#49

Post by lmkg »

bradbeattie wrote: post #39
jivatmanx wrote: post #27

Earlier quoted context omitted.

That's not strategic voting according to the definition. In both cases you're still voting for C, the candidate you like the most. "In voting systems, tactical voting (or strategic voting or sophisticated voting or insincere voting) occurs, in elections with more than two candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome.[1]" If you mean…

My decision to vote either 0/0/1 or 0/1/1 is explicitly to prevent my desire for B over A from causing B to win when C might have a chance. Whenever you have to consider the ballots of other voters, you're dealing with tactical voting.

Approval voting is immune to a particular definition of tactical voting, which is somewhat weaker than the traditional one. Which isn't perfect, but it's better than most other methods can offer.

Most traditional voting methods are preference systems: You take your N candidates and rank them from 1 to N. Every voter is assumed to have a "ground truth" preference of ranking. Tactical voting means that a rational voter may sometimes be encouraged to vote with a ranking other than their true preference.

The weaker criteria that approval voting satisfies is this: A rational voter can always make a rational vote by writing down their true preference ranking in order, drawing a line, and approving everyone above that line. In other words, there is no situation where a rational voter would want to vote A > B when their true preference is B > A. This is a significant bound on the effects of tactical voting.

As you correctly point out, the rationally optimal place to draw that line can be tactical. Nonetheless, there is a strong argument that this is "less tactical" than many other systems allow.

Re: Voting is a Sham Mathematically Speaking

#50

Post by Nursie »

gabemart wrote: post #37

I found this article quite frustrating. >Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman. I found this by far the most interesting assertion, but the examples under…

It's late and I'm tired but I think in the following situation -

49% vote Bush, 42% vote Gore, 9% vote Nader. All Bush voters prefer Nader over Gore (unlikely!). All Nader voters prefer Gore over Bush. Half of Gore voters prefer Bush over Nader.

  - If the election was Gore:Bush, Gore would win 51:49
  - If the election was Bush:Nader, Bush would win 70:30
  - If the election was Gore:Nader, Nader would win 42:58
The group prefers Gore over Bush (A over B) and Bush over Nader (B over C) but Nader over Gore (C over A).

That's my reading anyway.

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