[EM] Condorcet strategy spreadsheet (was, ...maybe it should be about Condorcet...)

Juho juho4880 at yahoo.co.uk
Sun Jan 31 14:56:36 PST 2010


Yes, I agree that strategic opportunities are rare, especially  
implementable strategies.

In the scenario that I presented I assumed that there are three  
relatively independent topics. Lets say that 33% of the population are  
unemployed. For them the #1 topic is "more jobs". Another third of the  
population are very religious and their theme is about something that  
their religion says, e.g. "no alcohol". The remaining third could be  
non religious materialistic people whose main theme might be "less  
taxes". All groups are very interested in their #1 goal, so second  
preferences don't play a big role. They prefer a candidate that  
supports their #1 target even slightly over a candidate that supports  
their second target but ranks their primary target last. The society  
is thus quite competitive in the sense that most people have clear #1  
goals that they are very interested of. This approach makes the  
grouping of ideas less important. The unemployed voters may be either  
religious or materialistic (as second preference). Religious people  
may be either afraid of losing their job or afraid of higher taxes (as  
second preference). And materialists may be religious or afraid of  
losing their job (as second preference).

It is enough if some portion of the population thinks this way in a  
situation that would otherwise (without them) be a close tie between  
the three candidates. This is a sufficient condition that leads to a  
natural (and not necessarily weak) cycle. Candidate C1 promotes "more  
jobs" but he/she must pick one of the remaining ones as his/her second  
theme (to try to get some second preferences from that camp). Same  
with the other two candidates. The candidates could make these choices  
(their secondary themes) based on how they feel themselves.

If we assume that there are three candidates that are strong enough so  
that they have good chances to win the election then the existence of  
a natural cycle might be quite "natural". If most opinions are on a  
linear (e.g. left -right) axis then cycles are not probable, but f  
there are more opinion dimensions in the society (and no dominating  
one), then cycles are much more natural.

I however agree that natural cycles are probably not common. Quite  
often there is e.g. a Condorcet winner. Having one or two candidates  
that will be close to winning the election is more common than having  
three or more such candidates. And when cycles occur they are often  
not stable enough to be used as a basis for clear strategic guidance.

I also note that even if there is a "2% chance of having a rational  
strategy available" the frequency of situations where in addition to  
the existence of this opportunity one can also implement this strategy  
successfully (and without too bad risks) will be considerably lower.

All in all, I'm still waiting for someone to present a scenario where  
some strategy would clearly work in a large real life Condorcet  
election.

Juho



On Jan 31, 2010, at 11:38 PM, Jameson Quinn wrote:

>
>
> 2010/1/31 Juho <juho4880 at yahoo.co.uk>
> One more addition / clarification.
>
> I wrote:
> > The three candidates just happened to plan their campaigns so that  
> they generate a cycle. That could well happen.
>
> One could say that it is not probable that those three candidates  
> would form such a cycle for the same reasons that voters usually do  
> not have such cyclic preferences. But for single candidates that is  
> much easier. And there may well be some minor things that change the  
> opinions. One candidate might e.g. have lost credibility on topic X  
> due to some personal problems in that area, or due to external  
> propaganda (if not planned so by the campaign office and the  
> candidate). Cycles are thus maybe not a very common pattern but  
> surely possible in typical real life situations.
>
> Generally, there are "natural alliances" in the voter population.  
> Issue A and B are, for whatever reason, seen as closer to each other  
> than they are to C (think of the at-times-contradictory grab-bags  
> that are classed as "left" and "right"). Campaign managers would  
> tend to council the A candidate to have a subfocus on B and vice  
> versa. This would make such cycles less probable than the ~8-20%  
> (depending on the model) they would happen by chance. Furthermore,  
> traditional polling would have a hard time detecting the cycle.
>
> Still, I admit its possible. Say all of the above factors cut it  
> down by only 50%, and the base probability is 20%. Under these  
> pretty-generous assumptions, a detectable cycle happens under 1 in  
> 10 elections. Now, you have to further assume that the polls are  
> accurate enough to detect who is the likely honest winner. At most,  
> you're at 8%. Now, you cut down to just the groups who have an  
> available strategy; together, they are less than 1/3 of the voters  
> (or else their candidate would be winning). So, as a voter, you have  
> a priori around 2% chance of having a rational strategy available.
>
> Really, it's not much.
>
> Jameson Quinn

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