## Math in Elections Part 3 — Delegates, Conventions and Kings.

Last time we talked about some problems with the primaries.  I wanted to mention one issue that can arise at the very end of the primary process because of a seemingly odd combination of convention rules.  The problem presents itself when the delegates convene to cast their votes to officially nominate their party’s candidate.

First consider the following very simplified election where there are three candidates: HotPants, ‘Zam and Z; and three voters:  Jaybert, GloryProne and Nick(i)Name.  Each voter ranked each of the candidates with a 1 for their favorite, 2 for eh, 3 for their worst enemy.  Here are the results:

So at this point, if everyone voted (assuming that we are using any semi-reasonable winner-declaring system), this race would of course end in a three-way tie.  But what if after some snooping around UCSD, Nick(i)Name learns how GloryProne and Jaybert are planning to vote.  Then, although she is unable to get ‘Zam, the true Man that she really wanted, she does have “King (Queen) Maker” powers.  i.e. she is able to choose the winner from among Z and HotPants.  Since Z is her worst enemy, she settles for HotPants (but what’s new, am I right? [jk, HotPants!]).

So the question is, when is there a King Maker?  And are King Makers necessarily a bad thing?

Assume there are three candidates in some heated election.  The election resulted in candidates $A$ and $B$ each getting 40% of the vote, while candidate $C$ received 20% of the vote.  Assume that in order to win, one of the candidates must get 50% + 1 of the vote.  Candidate $C$ has no chance to win in any scenario.  But what if the rules allow candidate $C$ to give his votes to any other candidate.  This may seem like an odd rule, but let’s go ahead with the assumption.

In such a scenario, candidate $C$ now has the ability to effectively choose the winner; $C$ is the King Maker.  In some sense this makes $C$ the “dictator” (as defined in Post 1) in a “new election”, in the following sense.  We can view the first election as resulting in no winner, and provided neither candidate $A$ nor $B$ is willing to concede, there is essentially a second election where there are two candidates ($A$ and $B$) and just one voter that matters ($C$).  We have already said that such a system is unfair in the first post of this series.

Now, there are some subtleties going on that make it a little different than the original dictatorial scenario.  If candidate $C$ simply votes for the candidate most similar to himself, then it would seem like the system more or less did choose a winner that is most representative of the people.  But no one expects this last step to be so pure.  You’d have to expect there to be some back room deal made and, because of that, this system seems rather suspicious.

Now, it may come as a surprise that what I just described is exactly how the presidential primaries work.  Each state holds a primary or a caucus.  And based on the results, some candidates are awarded delegates for the concluding party convention.  A candidate must get 50% + 1 of the delegates to be declared the party’s nominee.  However, here’s the catch: a candidate more or less has complete control of how his/her delegates vote.  Of course you would usually expect that candidate to instruct the delegates to vote for himself/herself.  But in a situation like the one described above, a candidate with no chance of winning among a field of candidates all of which failed to reach the 50% mark certainly could play King Maker if the number of their delegates is enough to push at least two of the other candidates past the 50% mark.

This was precisely Ron Paul’s goal this past year.  To collect enough delegates to be a player in the end, and hope that the field narrows down to Romney vs. A Single Conservative Alternative, in which case such a contested-convention scenario has a chance to arise.

The plan did not unfold as he hoped.  But for awhile it was a slightly reasonable possibility.  And so, indeed, this is a possible consequence of our poorly set up primary system that could, in some election cycle, cause many Americans to feel very mistreated by this non-democratic process.