Hello,

sorry if I arrive late. I just set up my masternode, and I am still having trouble with it. I am also writing a book on eDemocracy, and have been working on eDemocracy for several years now (at least from 2009 nearly full time, and interested from 2005). I am a mathematician interested in voting theory, I am actually writing a book on eDemocracy right now (you can find it and support me on Patreon).

The idea of voting with a number is the proposal I wanted to make, so well done in beating me on time on this. But it is very important that this is done well. And to do well you should not take the average, but the median.

I saw other people have suggested the median before but not everybody was able to defend it properly. So please let me do it for them.

The median, respect to the average have several qualities.

You know what a Condorcet Winner is? Basically when you have several options, the Condorcet winner is the proposal that wins all pair wise comparisons. In other words, if you have n proposals of which you are going to implement only one, given two proposals a, and b, a pairwise comparison between a and b measures how many people would prefer a to b and how many people would prefer b to a. A Condorcet winner is a proposal that is preferred respect to ALL other proposals. Not always there exist a Condorcet Winner. There are some loops where the majority of people prefer A to B, B to C and C to A. Which is weird at the beginning.

Now, there is a theorem, theorem of Black, or of the median voter, that in simple terms says:

If:

H.1) you need to decide a number

H.2) the number is on a one dimensional space

H.3) every person have their favourite number and how much they like the results goes down as you go away from that number

In other words if it is unidimensional single peaked.

THEN:

T.1) there exist a Condorcet winner among all the numbers,

T.2) if everybody votes for their peak, the median will be a Condorcet winner among all the numbers voted.

T.1 is already a really good result. There exist a condorcet winner, wow!, we have a solution. We don't need to find compromises where no majority likes. But the really good thing is T.2 that it is possible to calculate this number without having to ask everybody to vote with their whole spectrum (how much they like each possible number).

This is amazing. Now, the average does not have this property, and it does not have this property for some very clear reasons. The average is subject to strategic voting. Let me explain, if everybody has voted, and only I need to vote, and I know how everybody have voted I can pretty much manipulate the result by voting something very extreme. Suppose that we need to decide how much each proposal should cost. Now it is 5 dash, some people are proposing 1 dash, other 0.1 and so on. Suppose that you want a result being 2.3 dash, and the actual average is 2.1 dash, and 4235 nodes have already voted. Now you are the last one, you can pretty much calculate a number such that the resulting average is exactly 2.3. And if you are allowed to vote negative numbers you can also do the same trick going down.

Notice that this does not happen if you use the median.

So, great idea, congratulations. But make it the median, not the average.

Pietro Speroni

P.S. I am tempted to upload the file of the chapter of my book on this topic. But I just arrived and I am not sure how this would be taken

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