[EM] Later no harm, Condorcet, and randomization

[Kevin Venzke]

Jobst,

 --- Jobst Heitzig <heitzig-j at web.de> a écrit : 
> Since the topic of "Later no harm" came up again, I would like to point
> out that some randomization can make a Condorcet methods fulfil that
> criterion in a certain sense.

By the way, I think Later-no-harm is very important, in order to coax
information out of the voters, and avoid de facto Clone-Winner failures.

> In other words: If some amount of probability moves down in the voter's
> ranking, then below that position some amount of probability must also
> move up in the voter's ranking. In particular, the least preferred
> possible outcome can be no worse than before, so that voting later
> preferences helps avoiding the worst choices!
> 
> For a deterministic method, this is equivalent to "Later no harm", since
> then it just demands that the winner (=probability 1) cannot move down
> the voter's ranking, am I right?

I'm still digesting your suggestion. I believe Later-no-harm is normally
stricter than this, though: No candidate ranked above the new preference
is allowed to suffer a decrease in the probability of being elected, even
if that probability moves upwards in the voter's ranking.

But I don't think loosening this criterion would help much, since normally
if adding a preference can affect other candidates' odds of election, you
don't know whether these candidates are ranked above or below the new
preference.

A Condorcet winner always makes it into the CDTT set, incidentally. I
think that's good enough for me.

Kevin Venzke



	

	
		
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