Cardinal Condorcet voting method: Minumum Maximum Median

[parker friedland]

I have a voting system that I believe is much more fair then range voting. I call it Minimum Maximum Median (this system is similar to majority judgement and mini-max). It's not perfect but no voting system is. Here is how it works. My ballot contains my satisfaction of each candidate and is as follows:

Blue      |  ★★★★★

Green   |  ★★★★✰

Red      |  ★✰✰✰✰

Yellow   |  ✰✰✰✰✰

 

Poll workers then convert my ballot the differences in satisfaction I get if one candidate is chosen over another, which is this:

 

Red        ✰✰✰✰✰ | ★★★★✰   Blue

Red        ✰✰✰✰✰ | ★★★✰✰   Green

Red        ✰✰✰✰★ | ✰✰✰✰✰   Yellow

Blue       ✰✰✰✰★ | ✰✰✰✰✰   Green

Blue       ★★★★★ | ✰✰✰✰✰   Yellow

Green    ✰★★★★ | ✰✰✰✰✰   Yellow

 

Poll workers then release all the different candidate to candidate pair scores given by voters as well as their frequency at their voting booth. We can now use this information to find the winner of the election. The median pair scores for each of the fallowing candidate match-ups is as fallows:

 

Red        ✰✰✰✰✰ | ★★★✰✰ Blue

Red        ✰✰✰✰✰ | ★★✰✰✰ Green

Red        ✰✰✰✰✰ | ★★★✰✰ Yellow

Blue       ✰✰✰✰✰ | ★★✰✰✰ Green

Blue       ✰✰✰★★ | ✰✰✰✰✰ Yellow

Green    ✰✰✰✰✰ | ★✰✰✰✰ Yellow

 

Each candidate’s worst pairwise defeat scores are as fallows:

 

Red:   -3

 

Red        ✰✰✰✰✰ | ★★★✰✰ Blue

or

Red        ✰✰✰✰✰ | ★★★✰✰ Yellow

 

Blue:   -2

 

Blue       ✰✰✰✰✰ | ★★✰✰✰ Green

 

Green:   -1

 

Green    ✰✰✰✰✰ | ★✰✰✰✰ Yellow

 

Yellow:   -2

 

Blue       ✰✰✰★★ | ✰✰✰✰✰ Yellow

 

Green is the winner because green has the best worst defeat.

 

The reason this method uses a median to generate the pair scores is because it is fairer to an average and if we were to use an average, we would be giving voters an incentive to betrayal their favorite candidate because a voter’s two favorite candidates also must have a pair score between each other.

 

If you want to know how ties are resolved, they are resolved the same way ties are resolved in majority judgement.

 

Some of the pros this method has over range voting and majority judgement:

 

1. In a two way race, the candidate preferred will always win
2. It is very rare if possible for there to be a reason to not give your favorite candidate a higher score then your second favorite candidate (because you ranking your second favorite candidate lower than your favorite candidate will only hurt them in one pairwise median score: the one between your first and second candidate. The only way this could hurt your second favorite candidate is if that pairwise median score was their worst and the amount that you showed on your ballot that you preferred your favorite candidate to your second favorite was lower then this median)

 Some of the pros this method has over other Condorcet methods:

 

1. It obeys the favorite betrayal criterion unlike most Condorcet methods because you can give two candidates the same ranking

 Some of the cons to this method

 

1. It can pick a Condorcet loser (this may really anger hardcore supporters of Condorcet methods however it is important to keep in mind that it is possible for the best compromise candidate to occasionally be a Condorcet loser if that Condorcet loser is just liked slightly less then many voter’s favorite candidates).
2. It doesn’t always pick the result that gives a population the greatest satisfaction. This may also annoy some fans of range voting however I have never claimed that that is the point of this method and it is important to keep this in mind: #1. Range voting doesn’t accomplish this either because of strategic voting and #2. I believe that if it is possible to get voter’s honest satisfactions of candidates by sticking dopamine detectors into their heads, choosing a candidate with a great median satisfaction is generally better then choosing one with a great average satisfaction.)
3. It's more complicated and harder to implement in real life.
   

Why don’t you email me some more cons to this method. I would love the feedback. This method is still just a rough draft and can be improved.

[parker friedland]

You should add this to your web page because I have searched the internet for cardinal voting systems, and so far, I have only found three that are majoritarian  :  approval, range, and majority judgement.

I think it is important for people to know that there are more then just three cardinal voting systems.

[Spenser Kearns]

Ties seem pretty likely unless you increased the range to 0-99 or more. What would be the tie breaking procedure? Otherwise, I think this is pretty neat. You may be interested in Warren's thoughts on medians vs. averages. http://www.rangevoting.org/MedianVrange.html

[parker friedland]

Ties are broken the same way they are in majority judgement.

Here's how it works: you don't really compare all the candidate's worst median scores. That is an oversimplification. What you really have to compare is what I call a median ordinal.

let's suppose that this is all the satisfaction differences between red and blue:

Red    4, 4, 4, 3, 2, 0, -3, -3, -3, -3, -3, -4, -4,    Blue

The first median would be -3

Because there are an odd number of votes, we will remove 1 vote from the middle to get the second median:

Red    4, 4, 4, 3, 2, 0, -3, -3, -3, -3, -4, -4,    Blue

The second new median is -1.5
Because there are an even number of votes, we will remove 2 vote from the middle to get the second median:

Red    4, 4, 4, 3, 2, -3, -3, -3, -4, -5,    Blue

The third median is -0.5

Red    4, 4, 4, 3, -3, -3, -4, -5,    Blue

The fourth median is 0

Red    4, 4, 4, -3, -4, -5,    Blue

The fifth median is 0.5

Red    4, 4, -4, -5,    Blue

The sixth median is 0,

Red    4, -5,    Blue

The final median is -0.5

We can now turn this into a median ordinal by putting the values together:

(W means omega. If you don't know what that means, pretend W means 1 million.)

-3 + -1.5W^-1 + -0.5W^-2 + 0W^-3 + 0.5W^-4 + 0W^-5 + -0.5W^-6

or

-3 : -1.5 : -0.5 : 0 : 0.5 : 0 : -0.5

We then chose the winner by selecting the candidate with the best worst median ordinal. We compare these ordinals only by their fist value, unless they are the same, in which case, we move to the second value and so on.

On Fri, Feb 24, 2017 at 9:27 AM, Spenser Kearns <kear...@mymail.vcu.edu> wrote:

Ties seem pretty likely unless you increased the range to 0-99 or more. What would be the tie breaking procedure? Otherwise, I think this is pretty neat. You may be interested in Warren's thoughts on medians vs. averages. http://www.rangevoting.org/MedianVrange.html

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