Why iteratively eliminate candidates? (was Re: Housekeeping Lett

[Steve Eppley]

Donald D wrote:
-snip-
>   TWO: Why do I like to drop candidates?
>
>QUESTION TWO: "To Drop or Not to Drop - that is the question". We
>are only going to have one winner in a single seat election - the
>rest of the candidates are going to be dropped. An election is not a
>social event in which everyone is welcome to stay as long as
>possible and no one's feeling are going to be hurt - most of the
>candidates are going to be dropped.

Donald is obscuring the point of the question: he is now using "drop"
in a different way than he did before.  Before, he used it to mean
*iteratively eliminate* one or a few candidates at a time.  Now he's
using it to refer to the final result for each of the nonwinning
candidates.  That's a slippery discussion tactic, and maybe I should
design a "Slippery Definition Alert" box to re-use each time he does
this.

Every single-winner method satisfies the criterion that all but one
will be dropped, by definition.  So if it will please Donald to use
*any* method which drops all but one candidate, I invite him to join
the rest of us and advocate Condorcet, which drops N-1 candidates 
simultaneously, or Smith//Condorcet, which drops N-1 candidates in 
two stages.  :-)

>Some will be dropped before the general election by the instrument
>called the primary election. 

Assuming parties continue to use primary elections to eliminate some 
of their wannabes.  (See the other thread about "dropping primaries"
where we agree that the "iterative elimination" by primaries ought to 
be dumped in favor of a good general election voting method.)

>Of the ones that survive to the general election most will be
>dropped on the first tally because most single seat elections
>produce a winner with a majority on the first tally. 

Donald is using the term "first tally" but this is an undefined
term.  I presume he's referring to the clause which may optionally
be included in majority rule tally algorithms, which would check to
see if any candidate is top choice on a majority of the ballots.
(That optional clause may sometimes offer a shortcut to determining 
the winner, but sometimes it will slow down the process.)

Whether or not most single seat elections have historically produced
majority winners is irrelevant, since they used flawed voting
methods which deterred viable candidates from competing and deterred
voters from voting for their true favorites.  Good voting methods
allow more candidates to compete and be viable, by eliminating the
spoiler dilemma for the potential candidates and by eliminating the
lesser of evils dilemma for the voters, so given a good voting method
we can expect it will be a rarity when a candidate is the first
choice of a majority in an election for a powerful office.

>This leaves the contests that have no clear winner - but even at
>this point most of these candidates will be losers.

That begs the question: what's a valid way to determine which are
losers?  Donald has proposed flawed measurements (MPV or Coombs)
which ignore some of the voters' preferences and can easily drop
the "winner."  We can define a "clear winner": someone who is top 
choice of a majority.  We can define a "clear loser": someone who 
is last choice of a majority.

>     The sooner we detect one of these losers and drop him the
>sooner we reveal the winner. 

That's bogus logic on three grounds.  First, it implies that a 
sequential process will lead to a conclusion faster than a parallel 
process.  That depends on the specifics of the calculations involved.
Maybe an iterative elimination process can save time by not counting 
some of the voters' preferences, but a pairwise tally may benefit 
from parallel processing.  For the sake of argument, let's stipulate 
that MPV and Coombs will lead to a final result a few minutes sooner 
than a pairwise method.

Second, there's no reason to believe that it's a useful criterion for 
democracy that the winner be calculated a few minutes sooner.  We 
want a good winner, not a bad winner a few minutes sooner.

Third, the measurement for deciding which one to eliminate must be 
something which doesn't ignore the voters' preferences, or it's not 
going to "reveal" the "real" winner.

>How are we to detect one of the losers? In these unclear contests
>the run-off people will drop the last candidate of the first tally -
>the Coombs' people will drop the winner of the last set of
>selections - the Approval Voting and Borda people will not drop
>anyone until they declare a winner(with no majority)then they drop
>everyone else. The Condorcet people will do the most dropping of
>candidates. In each of their pairing run-offs the balance of the
>candidates are dropped. When they have a circular tie some of the
>solutions require dropping candidates. And when they finally declare
>a winner they also drop everyone else.

Again, Donald is using the term "drop" in changing slippery ways. 
The point of the question is: why does Donald prefer a method which
*iteratively eliminates* one or a few candidates at a time, rather
than a method which drops N-1 candidates all at once?

>     I am willing to consider other methods of detecting one of the
>losing candidates.

Note that Donald has not really answered the question.  He has
repeated that he wants to iteratively eliminate candidates, but the
closest he got to explaining why is that it might let us determine a
winner a few minutes sooner.  Since calculating the winner a few
minutes sooner is obviously a criterion of no interest to any of us,
we should consider the question effectively still unanswered. 

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)