[Election-Methods] USING Condorcet

[Kevin Venzke]

Hi Juho,

--- En date de : Lun 7.7.08, Juho <juho4880 at yahoo.co.uk> a écrit :
> > Hi Juho,
> >
> > --- En date de : Jeu 3.7.08, Juho
> <juho4880 at yahoo.co.uk> a écrit :
> >> That scenario was the simplest I could imagine.
> Only three
> >> candidates. One strong candidate but below
> majority, one
> >> weaker
> >> runner-up, and third clearly weaker candidate.
> This was
> >> also the most
> >> threatening scenario from burial point of view
> that I could
> >> imagine.
> >> Are there simpler and more threatening ones?
> >
> > Again, it isn't enough to isolate the scenario
> where the strategy
> > succeeds. What matters is the scenario where the
> strategy is worth
> > attempting.
> 
> Aren't we looking for scenarios where the strategy
> succeeds and are  
> therefore worth attempting? (except if fearing that the
> voters would  
> use some irrational strategies)

We're looking at scenarios where the strategy may succeed or the strategy
may backfire. When the strategy has no effect, it tells us nothing about
how wise the strategy is.

> > It is no consolation that the strategy does nothing
> when
> > the strategizers' candidate is the CW (due to a
> majority or due to
> > second preferences from the third candidate's
> supporters), or when  
> > creating a cycle doesn't change the winner.
> 
> Yes, no incentives here.

No incentives *either way*. That's why such scenarios make no difference
when analyzing the wisdom of the strategy.

> > The strategy has to hurt their own interests. Call the
> major  
> > candidates
> > A and B, with the third candidate being C. A voters
> will use burial
> > strategy. Why would they not?
> > 1. Because it could move the win from A to B:
> Impossible because this
> > would violate monotonicity.
> > 2. Because it could elect C: Only when the B voters
> use burial  
> > strategy
> > themselves. (We're assuming everyone will give
> full rankings of  
> > course.)
> >
> > Even though the strategy may hardly ever *work*,
> it's quite  
> > unlikely that
> > it will hurt to try it, unless the opposing voters are
> using it too.
> 
> Ok, but there must be a reason why the A supporters would
> use the  
> strategy and the B supporters would not.

If the A supporters believe B voters will not use the strategy, then the
A voters should use the strategy.

If the A supporters believe B voters *will* use the strategy, then they
have a choice of either letting B win, or else punishing the B voters by
using the strategy themselves.

I think that given a certain scenario, some percentage on both sides
would decide to use the strategy. Most of the time nothing bad will
happen. But I don't think it's clear that nothing bad would *ever* result
from this.

> > Compare with an IRV voter who uses burial because it
> feels right  
> > and isn't
> > expected to make any difference.
> 
> IRV has quite different strategic incentives. Also
> irrational  
> strategies are a potential area of study (although not the
> default case).

My point is not about IRV's incentives but about the fact that a strategy
that isn't expected to do anything might not be consciously insincere or 
even considered important.

> > I don't think you have to be a thief,
> > or even trying to deter thieves, to use this strategy.
> >
> > By the way:
> > C is a minor candidate who makes it onto the ballot
> without anybody
> > knowing much about him except his few supporters.
> 
> Yes, I guess we must pretty much assume so to make the
> strategy work.  
> Of course if there are only three candidates then also C is
> known by  
> all the voters although it may be clear that with sincere
> votes C has  
> practically no chances to win.
>
> > I guess you don't have
> > candidates like C in your country, since you always
> seem to speculate
> > about how many second preferences he would be getting
> in a real  
> > election.
> 
> I think I was at least in most places referring to second
> positions  
> in the sincere preferences and the impact of that with
> respect to the  
> strategic incentives that the voters have.

I know that. I don't think you understand me. What I'm saying is that C
is a type of candidate who doesn't get sincere second preferences, because
nobody is aware of his campaign. They may not even learn his name until
they see the ballot paper.

The reason I say that C is this kind of candidate, is that I find it 
extremely easy to imagine a scenario where it would be totally ludicrous
for A or B voters to fear that the other camp is *sincerely* giving the
second preference to C. That's why I say, maybe you aren't familiar with
this type of candidate.

> > Maybe Condorcet would encourage a better candidate
> than C to enter the
> > race (call him "D") but it's not clear
> that Condorcet would make C go
> > away or that there always would be a D candidate.
> >
> > Even if A and B voters "sincerely" give C a
> second preference,  
> > essentially
> > ranking the unknown option above the competition, I
> consider it hardly
> > any different from using burial strategy, in terms of
> its destructive
> > effect on the outcome.
> 
> Ok, any scenario with or without Condorcet winners will do.
> All we  
> need to show is that there are scenarios that are plausible
> in real  
> life (large public elections) and where use of burial
> strategy is  
> likely and successful (does more good than harm). 
> Do you have some  
> specific set of votes in your mind that we could analyse?

The same one. Everyone can be expected to cast full rankings because they
have been assured that it's safe. A>B>C and B>A>C (in no order) are the 
most numerous sincere preference orders. One of these types may actually 
make up a majority of the voters. C>A>B and C>B>A sincere rankings are
together much fewer. Sincere A>C>B and B>C>A rankings are fewer still.

What I suggest is that some quantity of each of the A>B>C and B>A>C
factions will believe they're (perhaps only slightly) better off using 
burial strategy than not. It's impossible to tell what that quantity would 
be, as there are pressures from both directions. The expectation that no 
one will use burial strategy is itself a pressure to use it.

In the purest successful scenario (where everyone in a faction votes 
together), which as you know looks roughly like:

45 A>C>B (strategic)
40 B>A>C
15 C>B>A (if they instead vote C>A>B, the strategy does nothing)

There is a sensible background story here in that the C voters appear to
be closer to B than A, and to eat into B's first preference total. If A
voters can guess that A will place first, they may be more likely to 
expect to gain from burial strategy. What would prove them wrong is if
the B voters defensively use burial strategy themselves. Would/should they?
Maybe they should just hope for C to use favorite betrayal if they like
B.

Kevin Venzke



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