[EM] RE : D2MAC can be much more efficient than Range Voting (corrected)

[Jobst Heitzig]

Dear Abd-ul Rahman,

you wrote:
> And it seems very weird to me that the Favorite of the first ballot 
> wins in that eventuality. Why not the most approved of all candidates 
> on the two ballots?
Over and over again: This method was devised to be a really democratic 
method
in the sense that it gives each voter full control over her share of the
winning probability: A ballot is drawn at random and the winner must be 
one of
those options approved on that ballot. That was the goal I started with.

The second ballot only comes into play in order to give voters a 
supported way
of trading their share of the winning probability: When the second ballot
approves something the first one approves, too, then one of these 
"compromise"
options will be elected. Only here comes an "efficiency measure" into play:
The approval score is only used to decide between those options which 
both drawn
voters consider acceptable.

If there are no such common approved options, the two voters cannot get to a
compromise both prefer to a coin toss between their respective favourite 
options.
Therefore one of those favourite options will be elected.
Since both ballots were drawn uniformly at random, it doesn't actually 
matter
whether in that case always the favourite on the first ballot is elected
(as specified in the method's definition) or always the one on the 
second ballot,
or both with equal probabilities.

Yours, Jobst