Score Voting re-weighted by voter credibility?

Hi there! This is a theoretical question, to replace a different question I asked.

Has anyone conceived of or read about a way to re-weight a voter’s ratings by their ‘credibility’?

For example, let’s say John rates Candidate A as 5/5, but John’s ‘credibility’ as a voter is only 50%. Sarah rates Candidate A as 1/5, but Sarah’s ‘credibility’ as a voter is 100%.

What should Candidate A’s score be?

Well, I am sure you realize this is fundamentally undemocratic but I have heard advocating for such a system. In fact arguments like this go all the way back to Socrates.

In theory, a representative government was intended to mitigate this. The next step is then to say that we need to account for the issues with electing a representative. Arguably, you would get better representatives if the people choosing them were more informed. There are several ways this can and is done

  1. Who votes? We exclude children, criminals and the mentally insane. Long ago it used to be only land owners and the educated who could vote. About 100 years ago it was moved to include soldiers then all men then all women. The trend is away form excluding people which I would think is good. Some want to go so far as allowing children and non-citizens to vote. I am not sure that there could ever be a fair way to draw the line to exclude who is informed enough to vote because being informed is not binary. There is however a fair bit of self selection. Clearly voter turn out rates are pretty low so people themselves are choosing not to vote. I would bet that this participation in voting is pretty strongly correlated with informedness
  2. Who people vote for. This is best expressed through the dichotomy of partisan voting vs candidate voting. If you are voting for a specific person then you have to compare them to another specific person. In some riding the differences in stances can be quite nuanced. Parties tend to have pretty different platforms and rely on simplistic wedge issues. I would think that the more candidate-centric an election is the more those who are not willing to understand the issues will self-select out of voting. This is a strong argument against the partisan form of Proportional Representation. However, it is also an argument against systems with heavy vote splitting like in FPTP since they lead to proxy party voting. By this I mean that when people are voting for a candidate they choose that candidate primarily based on the party. I would like to see a system where the number of candidates for each party exceeds the number of seats. Cardinal systems would likely produce such behaviour naturally.
  3. Strategy to reward the informed. Understanding polls and strategy can enhance your influence in many systems. This is often used as a negative to bash score voting. For example many people do not score anybody at the highest score but vote more honestly about their true feelings towards the candidates. This lowers their net influence. There are many reasons why somebody might do this but low informativeness and intelligence are clearly on the list. I have never seen a system designed to benefit the informed or intelligent but I would be interested in the work from a theoretical position.

I think what you are thinking is to try to quantify 1 and then weight the ballots accordingly. Most systems could deal with a weighted ballot pretty easily but as I said above quantifying that weight is impossible to derive in a fair way. I tend to think that the error from uniformed voters is normally unbiased but I do live in a country with a corrupt populist leader so I may be wrong. My strategy has always been method 2. Try to devise a system which lowers bad incentive, polarization and partisanship. I also think that many small elections are better than one big one. ie elect a parliament then a PM from them instead of going straight to a president. Large elections attract money and demagogues so I would not want a direct vote for somebody of such power. This is also why distribution of power is important but in the end you need something like a prime minister or president.

Hope this answers your question. If you just want the math for how to apply a weighted ballot to a specific system tell me the system.

re-weight a voter’s

It depends on the system, but in general if a vote is worth 50%, then it is sufficient to halve its weight before counting.

by their ‘credibility’?

What establishes a person’s credibility? What rules determine who can and who cannot vote?
I created this list of constraints that the rules should have:

  1. Utility: they must be applicable in the greatest number of policy areas.
  2. Wisdom: they must rule out ignorance and stupidity as much as possible.
  3. Non-subjectivity: they must not exclude or include political ideologies (therefore, they must not be able to be exploited).
  4. Simplicity: they must be as simple as possible to teach, understand and accept.

Excluding people based on culture doesn’t make sense for the following reasons:

  • Cultured people could still generate incorrect votes (if you misuse the information you have, the result is still wrong even if you have a lot of information).
  • There are no clear rules for assessing a person’s culture.
  • Having so much culture does not satisfy Simplicity (constraints 4).

The only thing that satisfies the 4 constraints indicated are logical fallacies.
I think the “voting license” should only evaluate how much a person can recognize fallacies (through a test).

Even banning the vote to certain categories without objective reasons (minors, etc) is not fair. In a company, only those who support that company decide, so all and only those who pay taxes can vote.

Thank you so much, great points @Keith_Edmonds and @Essenzia!

The system here is score voting. How would you mathematically re-weight score votes by voter ‘credibility’?

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The original vote awarded the points like this (range [0,10]):
[10,8,6,4,2,0]
If the voter is worth 50% (half), voting scores will also become 50% (half) of the original ones, that is:
[5,4,3,2,1,0]

Formula:
100% credibility → each score * 1
70% credibility → each score * 0.7
50% credibility → each score * 0.5
30% credibility → each score * 0.3
0% credibility → each score * 0

There is one extra detail you may have to add in. In addition to multiplying all the scores of voter X by X’s credibility, if you want the result as an average you also have to divide by the sum of all credibilities.

(This system, by the way, is still independent of sliding the range, so for example -5…5 is equivalent to 0…10.)

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Thanks everyone! I’m going to think about other ways to do this that don’t scale directly proportionally… e.g. 10 points @ 10% credibility and 1 point @ 100% credibility don’t necessarily need to equal the same result…

You can pass the credability through any funtion you want.

I think there is a place for this, but hopefully not for government elections. You might weight the vote of stockholders (or members of worker-owned cooperative) by how much equity they have. Seems fine to me, and perfectly democratic within such a context. (although I guess people will define “democratic” as they wish)

As for how to tabulate, it seems very simple.

To handle the initial scoring is, if they have 50%, you add .5 votes to the total, and multiply their votes by .5 when adding them up. When you average, you just divide by the total. (although technically averaging is unneeded, so you can skip much of this)

Then, when counting how many ranked A above B vs. B above A, you count the 50% person as .5 instead of 1.

Quite simple.

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I could see China using this with their social credit system. The way China is going lately I could see them going full dytopian nightmare next.

Why bother? Elections in China are already designed to achieve controlled outcomes. In any system where candidates must get permission to run, the only power voters have is whatever power the authorities in charge of permitting candidates decide to delegate.

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