[EM] Random and reproductible tie-breaks

[Steve Eppley]

Hi,

Raph Frank wrote:
> Stéphane Rouillon <stephane.rouillon at sympatico.ca> wrote:
>   
-snip-
>>  Tie-breakers have no need to be clone-independent. You cannot predict a tie
>> will occur
>>  before the election and it would be ridiculous to strategize on this
>> hypothesis.
>>     
>
> In fairness, tie breaks are a low probability issue in any case.  If
> you are going to do them right, you might as well do them fully right.
>   

Raph seems to be saying it's just an aesthetic value for the tiebreaker 
to be independent of clones.  I believe it's not just aesthetic.  
Stephane erred when he wrote it is ridiculous to nominate clones unless 
one can predict before the election that a tie will occur.  All that's 
needed for nominating clones to be strategically sensible, assuming the 
cost of nominating clones is low, is that the probability of a tie is 
not negligible.  The probability of a tie is typically not negligible 
when voting within small groups (committees, councils, legislatures, 
etc.) and the cost of nominating clones in small groups is typically 
tiny, which means it can be strategically sensible to nominate clones if 
the tiebreaker is not independent of clones.  It's a form of insurance 
against a low probability undesired event.

Even if one's focus is on large public elections, before asking the 
public to adopt the method in public elections it may be crucial for the 
voting method to first develop a track record of satisfaction among many 
small groups.  Hence the tiebreaker ought to be independent of clones 
(or should be close enough to independent that the probability of 
gaining by nominating clones is negligible).

I don't know that the tiebreaker used within small groups must be 
identical to the tiebreaker that would be advocated for large 
elections.  For example, in small groups a seniority system is common; 
typically a chairperson casts the tiebreaking vote.  Fortunately for us, 
that tiebreaker provides clone independence with repeatability and no 
randomness. 

Here's another tiebreaking option.  It's typical for groups to choose 
the status quo alternative when it's tied.  Perhaps it would be 
acceptable to break ties based on the order of nomination (treating the 
status quo as first nominated, when it's an alternative).  This 
tiebreaker wouldn't provide a strict independence of clones, I think, 
but it may be near enough to clone independent to make it strategically 
hard or pointless to nominate clones.  It too has the desirable 
attributes of repeatability and non-randomness.

In a more recent message in this thread, Raph wrote:
> Also, if there was a tie, then odds are that there is only 2 people
> involved, so it doesn't really matter about clones.
>   

I don't understand why Raph wrote that.  Assume a tie involves two 
alternatives, and assume the voting method (up to but not including the 
tiebreaker) is independent of clones.  By nominating clones of one (or 
both) of the two tied alternatives, the tie can be changed so it 
involves more than two.  It follows that it can matter whether the 
tiebreaker is independent of clones.

Regards,
Steve