[Election-Methods] a strategy-free range voting variant?

[fsimmons at pcc.edu]

Range Voting selects the option with the highest average rating.  Jobst has found a method that selects the option with 
the highest average rating by a random subset of the voters, while (totally?) discouraging the exageration of preferences 
that tends to happen in ordinary Range Voting.

It seems to me that it should be even easier to find a similar strategy free method that selects the option with the highest 
median rating; when a vote is above or below the median it makes no difference on the value of the median how far above 
or below (at least in the case of an odd number of voters).

The simplest idea is just to charge one voter grickle against the account of each voter that voted above the median of the 
winner, and redistribute these evenly to the accounts of the voters that voted below median.  Of course, lots of technical 
details would have to be worked out, e.g. to take care of the case where several options have the same median, and the 
case where nobody voted above median.  This version would end up being similar to some version of Bucklin with a tax 
for winning and a compensation for losing.

More analogous to Jobst's idea would be a method where a random ballot benchmark lottery is used, but instead of 
using the expected ratings of that lottery on the various ballots, use the rating R for which it is equally likely that the 
lottery winner would be rated above or below R (on ballot i).

If (on ballot i) the winner X is rated above R, then the probability P of the lottery winner being between R and X is the tax 
paid (by the compensating voters) on behalf of i into the accounts of the other voters.

Instead of voters with higher accounts having greater range possibilities, they would have greater weight in determining 
medians.

Also, the Random Ballot Lottery would take into account these weights.

Essentially, if your virtual bank account is 30, it is like having thirty votes, whether in the Bucklin aspect, or in the RB 
Lottery aspect.

I know that social scientists addicted to utility will prefer the mean approach over the median approach, but this makes 
more sense to me, because the "money" has a more direct relation to probability.

What do you think? Can something along these lines be worked out?

Forest