[EM] Re: open primary followed by election

[Araucaria Araucana]

On 26 Jul 2005 at 18:28 UTC-0700, Forest Simmons wrote:
> [Q] continued with comments and other suggestions, including the use
> of Jobst "direct support and also approved" style ballots in the
> primary, posing the question of how to make the best use of Jobst's
> ballots.

Let's use a standard term -- First Choice -- rather than "direct
support".  I meant to use the ballot format as the example, not the
terminology.

The use of approval in the first round has to have real weight behind
it.  It should penalize insincere approval of un-electable candidates
from the other side by giving non-first-choice approved candidates a
chance of knocking off your first-choice favorite.

My idea for a first round:

      candidate with > 50% first choice votes wins, no runoff

      Otherwise, candidate with highest approval >50% wins, no runoff.

      Otherwise, go to a 2nd round runoff.

This is like a variation of ER-Bucklin, isn't it?  With single vote
for 1st place, ER(whole) in 2nd-place, and no 3rd-place votes.  It is
also a little like one of Kevin Venzke's 3-slot methods.

Are you suggesting not allowing a winner at the first round?  Or do
you mean to use your second round method only if no candidate wins
more than 50% of first place votes?

>  
> I like this idea, and It seems to me that ranked ballots would not
> be necessary in the second round (the "runoff election") if the
> information from the first round (the primary) were used to form a
> reasonable lottery L as a standard of comparison.
>  
> Here's an example of how those ballots could be used:
>  
> 1.  After the primary (using Jobst style ballots) list the
> candidates in approval order.

Sure.  But this is really just sugar, a visual reminder to the voter
of how things stand.  Does it really penalize insincere approval?

>  
> 2.  Go down the list to the highest approval level at which a
> majority of ballots express approval for some candidate at or above
> that level.  Eliminate the candidates below that level.

I see this is an elimination stage, but I don't quite follow what's
going on here.  Say we're testing an approval elimination level of 5%.
Do 50% or more of the ballots approve any of the candidates above that
level?  How do I figure that out?

For example, say that seven candidates have approval > 5%.  Is there a
summable way to quickly see the fraction of ballots that approve at
least one of those 7 candidates?  Because of overlaps, this isn't the
same as adding up approval for each of the 7 candidates: I'd have to
count ballots that approve

     1 out of the 7
     2 out of the 7
     3 out of the 7
     4 out of the 7
     5 out of the 7
     6 out of the 7
     7 out of the 7

Not summable on the first count, right?  You need a recount.  Of
course, you'd only have to do this if the first round were not
definitive (again, what is your standard?), so it would be like doing
a recount anyway.  But I'd still like to see an example.

Not terribly understandable or publicly acceptable as it stands, I'd
say.

>  
> 3.  Form a lottery L in which the remaining candidates'
> probabilities are proportional to their direct supports.

Proportional with respect to the 1st-choice votes for non-eliminated
candidates, I assume?  This is less than the total number of ballots.

So how valuable is this lottery?  Does it make the 1st-place vote too
valuable?  Is going to encourage compromise in picking your
first-place candidate?

>  
> 4.  The second round is pure approval.  If no candidate receives
> more than 50% 

  ... second round ... (right?)

> approval, then lottery L is used to choose the winner.  Otherwise,
> the candidate with the greatest approval in the second round is the
> winner.
>  
> Note that in the second round, approval has a definite meaning: you
> approve candidate X iff you like X better than the lottery L.

So you approve a candidate X if you like the candidate better than
their odds in the lottery.  You would do this almost always (for a
favorite or compromise candidate) unless X had tremendous (if not
total) probability in L.

>  
> If there are N remaining candidates, it takes only N comparisons (of
> the form X?L) to fill out this approval ballot, whereas an ordinal
> ballot would take at least N*lg(N) comparisons ( of the form X?Y),
> where lg(N) is the integer part of the base two log of N.

Approval is certainly the easiest ballot of all the EM alternatives.
But the question is whether Approval will pick a better candidate
than, say, DMC.

> Note, also, that if L supports just one candidate X, then the only
> way that the lottery L can be the winner is if candidate X is a
> Condorcet Winner.

I don't quite follow this ... I gather that you mean that some
candidates W, Y and Z are included in the 2nd round with X, but none
of them get any first place votes, so L supports only X.

L is the winner iff none of {W,X,Y,Z} get higher than 50% approval.
The electorate is splintered, so the best we can do is pick a number
out of a hat.

>  
> In general (even when L gives probability to more than one
> candidate), the only time the lottery L will be used to pick the
> winner is when L beats every flesh and blood candidate by a majority
> of votes, i.e. when L is the Condorcet Winner, which means that a
> majority of the electorate prefers to take their chances with L over
> any individual candidate.

Mutual distrust, in other words.  Splintered.

>  
> It seems to me that this would be rare, but if it did happen, it
> would be lottery by popular acclaim, not by imposition of a lottery
> method per se.

When would recounts be necessary?  At the 50% level, for sure.  What
if there were tight margins at the approval elimination level in the
first race?  Couldn't that be a big delaying factor in deciding who
goes into the 2nd round?

>  
> The method could be nick-named AvTF for "Approve or Tempt Fate," or
> perhaps AvD for "Approve or Dare."
>  
> Comments?  Better ideas for the lottery L?  Better name for the
> method?

This is quite interesting ... what if candidate U gets 25% of the
1st-round first place votes, no approval from other voters, but the
1st-round approval elimination level is 26%?  It means there is no
broad consensus that U is fit to run for the office.

Name-wise, I think it should just be called 2-round Approval.  The
lottery should not be overly emphasized -- it is the tie-breaker in
case of < 50% approval.

Q
-- 
araucaria dot araucana at gmail dot com
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Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html