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.
Yes of course, but I consider strategic voting to be an advantage, not a disadvantage. It is very important to know what the other have voted, and to adapt to their votes, this is what the games theory states. You are trying to somehow "hide" this property, by introducing the median average, but this is wrong, because you accustom that way the voters not to watch of what the others have voted. In the system I have in my mind there is no one that votes the last. The polls are permanent and the voters can change their vote whenever they wish. So in general there is strategic voting, but no one is the last one who decides. This is valid for most of the governance decisions, which dont need to have a deadline. But of course there are some few cases where decisions need to have deadlines. In that case the strategic voting requires for the smart voters to vote the last minute, in order to be able to see what the other voters voted.
It is obvious that H.3 does not complies to the games theory, presupposes the total absence of strategic voting, thus it is a wrong premise. Do you know what a conditional vote is? The conditional vote is the correct premise.Now, there is a theorem, theorem of Black, or of the median voter, that in simple terms says:
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
We can solve the problem the mean average has with the people who cast very high number votes in order to screw the average. Excommunicate them! I really believe that the mean average is the best selection process, if it is combined with a threat of excommunication for those who are far away from the average. So you allow the freedom of choice, but you maintain the excommunication/ostracism threat for the individuals who constantly vote outrageous (of course the individuals who vote outrageous can protect their privacy, if a proof of individuality scheme is used) Excommunication/ostracism in the sense that they lose their voting rights, not their money. I am a proponent of the temporary excommunication/ostracism, which means that if the ones who vote outrageous change the voting that has been judged by the whole community as such, then they should automatically gain their voting rights again. The number voting has sense within some bounds , although @GrandMasterDash claims that the mean average is the cause of the bounds problem. And I claim that nature is always bounded, with the speed of light being the upper bound.
Of course excommunication/ostracism is always a very bad thing, thats why I am trying to solve that problem by introducing my mode average variation 2 selection process which is a combination of the mean average and the mode average.