[EM] Anyone got a good analysis on limitations of approval and range voting?

[robert bristow-johnson]

On Nov 25, 2009, at 3:26 PM, Kristofer Munsterhjelm wrote:

> robert bristow-johnson wrote:
>
>> my understanding is that the later-no-harm result happens only if  
>> the case of a Condorcet cycle (the prevalence of which i am  
>> dubious about).  where there is a Condorcet winner and that person  
>> is elected, is there still possible later harm?
>
> As far as I remember, Condorcet and LNHarm has the property that  
> LNHarm isn't, by itself, violated as long as there is a CW, but the  
> transition from CW to no CW (or vice versa) makes it inevitable  
> that there will be a LNHarm-violating discontinuity *somewhere*.

the degree of inevitability is an issue.  if "inevitable" is measured  
as a binary value, the i s'pose it's inevitable.  if "inevitable" is  
measured as a probability of a cycle occurring per election-year,  
then i think it's a small number.  if cycles are rare, the mean  
percentage of elections that have Condercet cycles is small.  when we  
somehow figure out a merit metric for an election system, a low- 
likelihood of a pathology that has low cost (say, if a cycle happens  
you elect using IRV rules, how bad can that be?) should contribute  
(negatively) negligibly to the merit metric.

> In other words, as long as you stay within the CW domain, there is  
> no LNHarm failure, but there is no way to engineer a completion  
> rule to maintain this for every CW<->no CW transition.

sure, but i'm still dubious about the product of likelihood times  
cost of occurrence of that.

> I'm not entirely sure about that, though - can anyone confirm?

and i continue to wonder (really) how a possibly rare occurrence of a  
no-CW election (with its LNHarm consequence) becomes a greater  
concern than that of the likelihood and cost of electing a candidate  
against the expressed wishes of a majority of the electorate.  i  
think that cost (electing the wrong candidate) is reasonably high and  
that the likelihood of it happening is definitely non-zero because it  
has happened in the Vermont town i am a resident of.

> Not that this bothers me - LNHarm seems to me to be a criterion of  
> "don't take the full picture into account". Consider a negotiation  
> situation: if everybody keeps their cards close to their chests  
> (i.e. vote bullet style), there can be no compromise; but if  
> they're willing to reach further, one might find an option that,  
> while not the favorite of any, is good enough for all.

i would call that the essential measure of a popular election.  it's  
utilitarian: we maximize satisfaction for the franchised about the  
governance of whatever organization by pleasing more people with a  
decision than we displease.  that's the reason we have elections, we  
could adopt rules to give it to the minority candidate if that  
candidate reaches a certain threshold, but we don't do that for  
binary decisions, we consistently give it to the majority.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."