Could Splitting Votes Lead to a More Accurate Election Outcome?

[causalset]

Have anyone ever considered the following voting system. Each persion is allowed a TOTAL of one vote. But that one vote can be ''split'' between candidates. So a person can say, for example, that 1/2 of the vote goes to candidate 1, 1/4 goes to candidates 2 and 3, while candidate 4 doesn't get any vote. And that's just an example. A person is allowed to come up with his own way of ''spliting'' his vote however way he chooses. To make his job easier, the numbers he enters will be normalized by the mashine. So, for example, a person can put number 7 next to candidate 1, number 5 next to candidate 2 and number 2 next to candidate 3. Then mashine will automatically say that he gave 7/14=1/2 vote to candidate 1, 5/14 vote to candidate 2 and 2/14=1/7 vote to candidate 3.

I just think this way of voting would allow more accurate assessment of whom people really want to be elected. For example, suppose candidates A and B have nearly the same politics that people favor; on the other hand, candidate C has ''unfavored'' politics. Now, suppose that the politics of candidates A and B are so similar, that people who ''favor'' them have very hard time deciding whom to vote for. So they all decided to pick A instead of B because A is younger and has more energy. As a result, candidate C will do better in the election than candidat B. But that is not an accurate estemation of people's opinion: after all, if A wasn't running, then ALL of the votes for A would have gone to B and B would have won over C by substantial margin. Now, if we have the kind of voting I propose, this would never happen. In this case people would simply split their votes between A and B, hence we would get accurate picture that both A and B are doing better than C.

Now you might ask: wouldn't each individual person be deciding to give ''all'' of his vote to his top choice rather than spliting it, anyway? Well, not necesserely. If a person favors two candidates, he might want to ''cover all bases'' by making sure that if one of them is going to lose, the other would win. That would be a motivation in spliting vote. Or for exaple suppose one of the candidates is Hitler, so our foremost goal is to prevent Hitler from winning, while the choice between other candidates is secondary concern. Well, voting for just ONE person ''other htan Hitler'' might prove to be ineffective if it turns out that that ''one person'' obtained substantially less votes than Hitler did. Thus, the most effective strategy would be to split a vote between all candidates other than Hitler so that if one of them won't win the other will.

Now, of course, what I just said will vary greatly depending on people's awareness of public opinion and so forth. So in some situation people might, in fact, choose to give all of their vote to one person. But still, at least there has to be an option of spliting a vote if someone wants to do that.

 

[Jimmy Snyder]

It wouldn't work. Bumper stickers aren't big enough. Don't blame me. I voted 2/5 for Romney, 1/5 for Obama, 1/5 for McCain, and 1/5 for Hillary.

 

[causalset]

It wouldn't work. Bumper stickers aren't big enough. Don't blame me. I voted 2/5 for Romney, 1/5 for Obama, 1/5 for McCain, and 1/5 for Hillary.

Doesn't have to be stickers. In fact I think more in line of a computer. I imagine a computer in a voting booth and a person should enter numbers on the keyboards next to candidates. Then when he presses enter key, the numbers are automatically being normalized (thus assuring total of 1 vote) and added to the respective candidates.

 

[MarcoD]

Well, if we're going to go 'crazy' on it anyway. Why not a voting system where you don't vote people in, but vote people out?

 

[Mech_Engineer]

OP: What specific problem do you think your proposed system solves? It seems to me like it's a whole bunch of extra complexity with no useful advantage. People can just decide which candidate they prefer, and vote based on whatever system they use to weigh their decision.

 

[Gokul43201]

For example, suppose candidates A and B have nearly the same politics that people favor; on the other hand, candidate C has ''unfavored'' politics. Now, suppose that the politics of candidates A and B are so similar, that people who ''favor'' them have very hard time deciding whom to vote for. So they all decided to pick A instead of B because A is younger and has more energy. As a result, candidate C will do better in the election than candidat B. But that is not an accurate estemation of people's opinion: after all, if A wasn't running, then ALL of the votes for A would have gone to B and B would have won over C by substantial margin. Now, if we have the kind of voting I propose, this would never happen. In this case people would simply split their votes between A and B, hence we would get accurate picture that both A and B are doing better than C.

There is no practical benefit to knowing the actual popularity of the unpopular candidates, is there? All we care about is that the system accurately select the most (electorally) popular candidate. Your proposal might alter the vote tallies so they more accurately tell you who was more popular among the losers, but it still produces the same winner as the existing system, doesn't it? At least in your above example, it does. Or maybe you can give us an example where it produces a different winner?

PS: Jimmy was making a joke. Bumper stickers are things that people stick on their cars to tell the world something about themselves.

 

[causalset]

Well, if we're going to go 'crazy' on it anyway. Why not a voting system where you don't vote people in, but vote people out?

Good idea. Here is how we can accomplish this. Each person can put either positive OR negative numbers next to each candidate. The normalization will be a division by sum of ABSOLUTE VALUES of the numbers a person put. Thus, if there are three candidates, and I put 5 next to A, 7 next to B and -15 next to C, then the normalization constant will be 5+7+15=27; thus, a candidate A will gain 5/27 points, candidate B will gain 7/27 points and candidate C will LOSE 15/27 points.

 

[causalset]

There is no practical benefit to knowing the actual popularity of the unpopular candidates, is there? All we care about is that the system accurately select the most (electorally) popular candidate. Your proposal might alter the vote tallies so they more accurately tell you who was more popular among the losers, but it still produces the same winner as the existing system, doesn't it? At least in your above example, it does. Or maybe you can give us an example where it produces a different winner?

Okay here is an example where it produces a different winner:

1. Democrates would like either A or B to win, without having any strong opinion between one or the other

2. Republicans would like either C or D to win, without having any strong opinion between one or the other

3. If C or D is to win, democrates would prefer that it is C rather than D

4. If A or B is to win, republicans will prefer it is A rather than B

5. Candidates B and D look younger and more energetic than candidates A and C, which slightly tilts vote in favor of the former

Now, if we have ''standard'' voting system, then items 3 and 4 would not affect the election result. Thus, the only factors that would affect results are 1, 2 and 5. The items 1 and 2 have no bearing on (A, C) vs (B, D). The item 5 says candidates B and D are ''better'' in some way. Thus, the president would be either B or D.

On the other hand, if we introduce MY system of voting, then items 3 and 4 will begin to affect the election results as well. In fact, items 3 and 4 will ''outweigh'' item 5. Thus, the president will be either A or C.

 

[causalset]

OP: What specific problem do you think your proposed system solves? It seems to me like it's a whole bunch of extra complexity with no useful advantage. People can just decide which candidate they prefer, and vote based on whatever system they use to weigh their decision.

Well one example of a problem that it solves is when people can't decide between two candidates. In this case, we don't want a ''random choice'' to have as much effect as well informed decision. So we give them another option: they don't have to flip a coin, they can just split a vote.

 

[Gokul43201]

That's a better example (#8), thanks. Lunchtime over - will think about it later.

 

[skeptic2]

It would also solve the problem of 3rd party candidates splitting the vote of one of the other parties. Examples: It is likely that the reason George H. W. Bush lost to Clinton was that Ross Perot took more votes from Bush than he did from Clinton. It is also likely that Gore lost to George W. Bush because Ralph Nader took more votes from Gore than he did from Bush. Would Romney be as popular if there were only one real conservative candidate to choose from?

 

[Office_Shredder]

There's no difference between two candidates splitting the votes in the current system and two candidates splitting the vote in your system. If Democrats like candidates A and B, and Republicans like candidates C and D, if the Democrats all split their votes between A and B the Republicans can just all vote for C and make him the winner, even if the population is 3/5ths Democrat and 2/5ths Republican.

It seems like this voting system is designed to solve problems that aren't the problem with our current voting system, namely that voting for someone other than the main Republican or Democrat is a waste - only now you can waste half a vote instead of a full vote

 

[MarcoD]

What are the problems with the US voting system?

 

[causalset]

There's no difference between two candidates splitting the votes in the current system and two candidates splitting the vote in your system. If Democrats like candidates A and B, and Republicans like candidates C and D, if the Democrats all split their votes between A and B the Republicans can just all vote for C and make him the winner, even if the population is 3/5ths Democrat and 2/5ths Republican.

No, what I said is that in my voting system democrates will be able to help C get ahead of D, despite the fact that both C and D are republicans. This can be done because democrates can use ''bigger'' portion of their votes for A and B, while reserving ''smaller'' portion for C and D, just in case A and B were to lose. This requires vote splitting. After all, each individual democrate cares more about voting for A and B rather than ''what if they are to lose''. So if votes couldn't be split, republicans would be the only ones voting for C and D. While if votes can be split, democrates will vote for C and D as well. Now, if C and D appeal equally well to republicans, while democrates have clear preference of C over D, then the REPUBLICAN candidate C will win due to DEMOCRATE vote, BUT ONLY IF votes can be split.

If Democrats like candidates A and B, and Republicans like candidates C and D, if the Democrats all split their votes between A and B the Republicans can just all vote for C and make him the winner

If you read the example more closely, the republicans have slight preference towards D over C (this is due to their ''indifference'' in part 2 combined with candidate D slight advantage mentioned in part 5). So if republicans are the only ones voting for C and D, then D would be a winner. BUT the democrates have HUGE preference towards C over D. So if democrates can offer fraction of their vote, then the candidate C will win. But their ability to make candidate C win is dependant upon splitting of vote since their top preference is to vote for either A or B.

 

[turbo]

I would much prefer that the US adopt the instant runoff system, in which voters get to make ranked choices, and the candidate with the lowest vote tally is eliminated between rounds. I believe that would have prevented the election of our Tea-Party governor. He got 38% of the vote, but a majority of voters preferred the Democrat (Libbey Mitchel) or the moderate Independent (Elliott Cutler). The one with the lower vote total would have been eliminated in the first round, and the other would have been inaugurated.

 

[causalset]

What are the problems with the US voting system?

Here is the example of a problem. Suppose more people voted for A than for B. But also suppose that people who did NOT vote for A actually hate A, while people who did NOT vote for B are semi-positive towards B but would rather have some other candidate. Now in light of this, it would actually be more fair towards general population to elect B rather than A. This, however, can only be done through split votes. The fact that candidate A is ''hated'' more than candidate B implies that candidate B would receive more fraction-votes from people who would otherwise not vote for him, which would allow him to win.

 

[causalset]

I would much prefer that the US adopt the instant runoff system, in which voters get to make ranked choices, and the candidate with the lowest vote tally is eliminated between rounds. I believe that would have prevented the election of our Tea-Party governor. He got 38% of the vote, but a majority of voters preferred the Democrat (Libbey Mitchel) or the moderate Independent (Elliott Cutler). The one with the lower vote total would have been eliminated in the first round, and the other would have been inaugurated.

Ranked choices is certainly ''better'' than only one choice, but still ''not as good'' as what I am proposing. Suppose you like nearly the same your top two choices, while you like the third and fourth choice a lot less. In this case, you can not indicate this by merely ranking them; you can, however indicate it by splitting your vote in appropriate way.

 

[turbo]

The great part about instant runoff is that you don't split your vote. Fanatics wouldn't split their vote anyway, in the hopes of getting their party's candidate into office when other voters split their votes. Indicating ranked preferences increases the chance that you will get a candidate elected that is preferable or at least acceptable to you.

 

[Mech_Engineer]

I'm starting to see the arguments for the weighted system, but let's be honest I'm not sure the added complexity and confusion would really bring enough added value.

I think when it comes down to it politicians try so hard to be ambiguous and general these days! if you have two candidtaes they each get about half the vote, if there are three candidtaed they each get about a third of the vote... People vote for whomever they like best on TV regardless!

 

[cmb]

Sounds like you'd achieve the same result as some existing variations of the Single Transferable Vote scheme.

Try looking up some of these voting schemes, see if you like them;

Gregory method,
Meeks method,
Warren method,
Hare-Clarke method,
Wright method,

and if you are doing internet searches, combine these terms with the words 'Droop quota', and that should pull up the links to these [and other] schemes.

 

[Gokul43201]

Here's another test of the Causalset method:

Consider the case of 3 candidates: A and B are essentially identical moderates, liked equally by a large fraction (nearly 2/3rd) of the electorate, while C is an extremist with a significant, though smaller group of supporters (a little over 1/3rd of the electorate).Current Method:

A and B split votes from their supporters, while C takes the rest.
Fraction of total vote that A gets, $V(A,total) = 1/3 - \Delta$
Fraction of total vote that B gets, $V(B,total) = 1/3 - \Delta$
Fraction of total vote that C gets, $V(C,total) = 1/3 + 2\Delta$

C wins the election for arbitrarily small positive $\Delta$. For instance, C wins if $V(A,total) = V(B,total) = 0.333,~ V(C,total) = 0.334$

That doesn't sound terribly fair to me. There are 2 candidates that appeal to a large majority of the voters (how often does that happen in real life?), yet they both lose to the one extremist that appeals to a much smaller plurality.Causalset Method:

One plausible scenario: Supporters of A and B (let's call them 'group ab', and say they make up the same fraction of the electorate as above, namely $2/3 - 2\Delta$) give each of their equally favored candidates a score of +1 (normalized to +1/3) and give C a score of -1 (normalized to -1/3). Supporters of C (call them 'group c', making up $1/3 + 2\Delta$ of the electorate) give C a score of +1 (normalized to +1/3) and give each of A and B a score of -1 (normalized to -1/3)

$V(A,total) = V(A,ab) + V(A,c) = (2/3 - 2\Delta)(+1/3) + (1/3 + 2\Delta)(-1/3) = 1/9 - 4\Delta/3$, where $V(X,y)$ is the share of X's total vote-fraction coming from 'group y'.

Similarly, $V(B,total) = V(A,total) = 1/9 - \Delta$

And $V(C,total) = V(C,ab) + V(C,c) = (2/3 - 2\Delta)(-1/3) + (1/3 + 2\Delta)(+1/3) = -1/9 + 4\Delta/3$

For C to win this election, it would require that $-1/9 + 4\Delta/3 > 1/9 - 4\Delta/3$ or $\Delta > 1/12$. So, C would need to have the support of at least half (1/3 + 2/12) of the population in order to win.

Sweet! I like that. Note that I didn't try to optimize strategies for 'ab' or 'c' - I just did the lazy thing and guessed what might be close to an optimal strategy. I wonder if my guess was indeed optimal. An alternative guess would be for 'group ab' to vote (A=0,B=0,C=-1), and maybe 'group c' goes with (A=0,B=0,C=+1). Someone with a little free time might crunch those numbers, or see if 'ab' and 'c' can independently optimize their votes, and figure out what does.

Or better still, does someone have a nice situation where the Causalset Method produces a less desirable result than the Current Method?

 

[causalset]

Here is more general pattern. Suppose we have extreme republican, mild republican, mild democrate and extreme democrate. If people could only vote for one person, the democrates will split EVENLY between mild democrate and extreme democrate. Likewise, republicans will split EVENLY between mild republican and extreme republican. If votes can't be split, all democratic votes would go exclusively to democrates, thus ''mild republican'' and ''extreme republican'' would be equally likely to win. Likewise, since all republican votes will be exclusively republican, mild democrate and extreme democrate would be equally likely to win, as well. On the other hand, if the split votes are allowed, then democrates would give ''split vote'' to mild republican in order to prevent extreme republican from winning, and republicans will give ''split vote'' to mild democrate just to prevent extreme democrate from winning. Thus, my way of voting will ''shift'' the elected candidates ''even closer'' to the middle and ''further away'' from extreme left or extreme right.

 

[Office_Shredder]

Gokul, the voters for C totally blew it in your scenario. It's more efficient for them to just put all their vote in for C (If they ding both candidates A and B, each C voter is only worth 2/3rds of a vote for C essentially)

Let's consider that situation - the voters for A and B split their vote three ways and the voters for C go all in for C:

$$V(A) = (1/3-\Delta)*2/3 = 2/9-2\Delta/3 = V(B)$$

$$V(C) = 1/3+2\Delta-(1/3-\Delta)*2/3 = 1/9+4/3\Delta$$

so C will win as long as $$\Delta > 1/18$$ in this situation.

The best case scenario for the voters for A and B, if they really don't care, is to just give a -1 to candidate C. Then candidate C can never win unless he has an outright majority, and the winner of A vs B will be decided by whatever pitiful fractions of votes the non-rational voters toss their way.

So candidates A and B, knowing that they want one of them to win, could run on a campaign of: give C a -9 vote and give your favorite candidate a +1 vote. C will be guaranteed to lose but A or B will win depending on who has more support amongst the non-C voters

 

[Gokul43201]

Gokul, the voters for C totally blew it in your scenario.

That was my suspicion. Thanks for doing the legwork.

It's more efficient for them to just put all their vote in for C
...
The best case scenario for the voters for A and B, if they really don't care, is to just give a -1 to candidate C.

I suspected (as I was finishing up the last post) that this might in fact be the case. Which is why I suggested it in passing, at the end of my last post.

An alternative guess would be for 'group ab' to vote (A=0,B=0,C=-1), and maybe 'group c' goes with (A=0,B=0,C=+1).

Now, with a pen and paper I see that this is indeed their optimal solution - lucky that it turns out to be quite easy to optimize their strategy. And I find it nice that with both groups voting optimally a majority is required for C to win.

 

[Vanadium 50]

There is something about voting systems that causes everyone to think there is no need to read up on what previous work has been done. I recommend everyone take a look at something called Arrow's Theorem, which proves that an ideal voting system cannot exist. Given that, the discussion should be centered around the faults of the proposed replacement being less severe than the faults of the baseline.

 

[cmb]

I recommend everyone take a look at something called Arrow's Theorem

Thanks for reminding me of that name. I've been trying to recall it recently in conversation when describing these proofs.

which proves that an ideal voting system cannot exist.

Well, let's be specific, it proves an ideal voting system cannot exist, given the axioms he used.

...and I believe there is a quite simple way to change the axioms, given the advent of modern electronic voting systems:

A scheme to break Arrow's axioms I tend to propose (when in discussion on this topic) is to have a system whereby [electronic] voting begins a week before the vote is counted. When you go to place a vote, you are presented with the votes cast to date. Then you vote.

Some will vote early, who have already decided firm who they want. Their advantage in doing so would be to show others that a minor candidate that others might not feel would get any support is getting it. That would encourage the group who would prefer that choice but would otherwise tend to make another choice to avoid their least favoured candidate.

Those who favour some head-strong character might want to try to sneak in at the last minute because if the running result was all biased to some extreme character the next voter in the booth might then choose to vote tactically against him.

I'm not at all sure how this would work out in practice, but having a voting scheme with a running total breaks the axiom of a fixed set of 'decision criteria' in the theorem, because instead you end up with a practically limitless number of non-independent decision criteria according to that of the voter and also of the running state of the vote.

 

[Gokul43201]

Their advantage in doing so would be to show others that a minor candidate that others might not feel would get any support is getting it.

How would they show this? The only possibility I can think of is exit polling. Right now, it's possible for say CNN to get good exit polling numbers because they need to hang out at polling stations for only a day. I wonder if they'd still want to do it if they had to spend a whole week camping outside polling places, talking to a much slower trickle of people. I suppose a candidate with a vested interest in these numbers might pay for the service but that could then raise doubts about bias.

 

[cmb]

How would they show this?

It is an idea dependent (actually, inspired by) electronic voting. When the voter is presented with a touch-screen to vote on (on on-line selection), next to each candidate would be the running total to date.

 

[Office_Shredder]

People overrate Arrow's theorem. Consider the idealized one dimensional political axis, where everyone's political position is a number between 0 and 1, and everyone votes for the politician who is closest to them on the scale, and there are two candidates, the median voter is a dictator. Does that mean that majority wins when having two candidates face off is unfair or not ideal? I would guess most people say no

 

[cmb]

People overrate Arrow's theorem. Consider the idealized one dimensional political axis, where everyone's political position is a number between 0 and 1, and everyone votes for the politician who is closest to them on the scale, and there are two candidates...

Then Arrow's theorem doesn't apply. It relates to voting for 3 or more options.

 

[Office_Shredder]

The statement of Arrow's theorem is: if blah blah blah about voting systems, then there is a dictator. People gasp. Oh my god, a dictator! They scream. But the system I described has a dictator, and nobody thinks that's a terrible thing.

 

[cmb]

The statement of Arrow's theorem is: if blah blah blah about voting systems, then there is a dictator. People gasp. Oh my god, a dictator! They scream. But the system I described has a dictator, and nobody thinks that's a terrible thing.

I think the terrible thing about this is your understanding of Arrow's theorem!