[EM] DH3 and honest Condorcet winners

[Kristofer Munsterhjelm]

On 7/18/21 6:03 AM, robert bristow-johnson wrote:
> 
> 
>> On 07/17/2021 1:31 PM Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
>>
>>   
>> In the classical DH3 scenario, the dark horse is universally loathed by
>> the voters. This suggests a smart-aleck way of making almost every
>> method DH3-proof: just eliminate every candidate that don't have at
>> least one first preference.
> 
> which, if you have 10,000 voters will never happen.  try flipping a
> coin and get heads 50 times in a row.  that's more likely to happen.
> 
>>
>> Now suppose that we have an election after every faction has gone on its
>> burial spree,
> 
> so voters are upping the Dark Horse that they loathe in an attempt
> to  gain advantage over the other candidates they fear will beat their 
favorite?
> 
>> and there were initially some voters who ranked the dark
>> horse first. It would look something like this:
>>
>> 34: A>X>B>C
>> 33: B>X>C>A
>> 32: C>X>A>B
>>   5: X
>>
>> But this is just a three candidate version of the Left, Center, Right
>> scenario. If X is a genuine consensus candidate, then X should be
>> elected
> 
> and i cannot see how you can differentiate this scenario from the
ostensible Dark Horse insincerely bumped up.

That was my point. If you want Condorcet, you can't just exclude 
candidates with few first preferences. So the only remaining option to 
resist DH3 is to make the burial not pay.

> Arrow or Gibbard or Satterthwaite aside, we should examine what are
> common or likely scenarios that would incentivize strategic voting and
> not use contrived and highly unlikely specific scenarios in policy
> making to evaluate voting systems.
> 
> it's the most threatening hazards that we should try to avoid.
> 
> outside of a cycle, and valuing equal voter influence in elections,
> what is a *realistic* hazard that would challenge the main election
> ethic of elections, that is to determine the majority will of the
> electorate and elect a candidate so that the minority voters' votes do
> not count more than the majority voters' votes?

The thing is, we don't know, because Condorcet methods have been used so 
little. On the one hand, when Wikimedia used Schulze, they had no 
problems with strategy, and they chose to replace it with Approval for 
complexity reasons alone. So if they're anything to go by, any advanced 
(Smith, strategic entry/exit resistant) Condorcet method will do.

On the other hand, people *worry* that e.g. mass burial will happen. The 
whole DH3 scenario is based on Warren's experience with Borda, which is 
inordinately susceptible to Burial. On the face of it, it might seem 
absurd that two thirds of the voters would preemptively bury opposition 
candidates under someone nobody likes. I don't think it would happen in 
Condorcet, but some people do.

So e.g. DH3 resistance or DMTBR is then less about resisting strategy we 
know will happen, and more as insurance: to say to the people who think 
that the voters would mass bury, that there's no incentive to do it 
under *this* method.

Then the people can choose: do they want excellent results with honesty? 
Then Ranked Pairs. Or do they want to be insured against strategy? Then 
Smith-IRV, Pb, whatever.

But in practice, if you're aiming for a particular Condorcet method... 
any Condorcet is better than no Condorcet! (Well, pathological methods 
notwithstanding.)

-km