Certainty

 

Blue Christmas

I'll have a blue Christmas for certain
And when that blue, blue heartache starts hurtin'|
You'll be doing alright with your Christmas of white
But I'll have a blue, blue Christmas

How certain are you?

Ranked choice voting is about compromising, finding a common ground to achieve certainty.  Winner takes all voting is only about dominance, not certainty or compromise. 

Take a voting slate of four candidates, (A, B, C and D) and ranked ballots from eight voters to choose the most acceptable candidate to those voters. The ballots by voter are as in the table below.

Voter
	1	2	3	4	5	6	7	8
1st Choice	A	C	B	C	B	A	C	D
2nd Choice	B	B	A	A	A	B	A	C
3rd Choice	C	A	C	B	D	D	B	A
4th Choice	D	D	D	D	C	C	D	B

From only the First choices, Candidate A has 2/8 of votes, Candidate B has 2/8 of the votes, Candidate C has 3/8 of the votes and Candidate D has 1/8 of votes.  Candidate C is 100% the most dominate candidate if only First Place votes are considered.  However certainty is not the outcome with the highest total.  It is the certainty of the outcome with the highest total multiplied by the probability of that outcome.  In that case Candidate C is has a certainty of less than 24% if only First place finishes are considered.

Candidate Points					Candidate certainty
A	B	C	D	Points	A	B	C	D
2	2	3	1	8	18.8%	18.8%	23.4%	10.9%
8	7	7	2	24	44.4%	41.3%	41.3%	15.3%
16	14	13	5	48	66.7%	62.0%	59.2%	28.0%
24	22	21	13	80	63.0%	59.8%	58.1%	40.8%

If the First and Second place votes are counted, with 2 points for First place and one point for Second place, for a total of 24 possible points, then Candidate C is no longer the dominant candidate. In fact that Candidate is now tied with Candidate B.  The most dominate is Candidate A and the certainty that this is the preferred Candidate of all voters is over 44%.  If 1 point is awarded for Third place, 2 points awarded for Second place, and 3 points are awarded for First place, then the dominant candidate is still Candidate A, but the certainty that this is also the preferred Candidate has increased to almost 67%. Increasing this to 1 Point for Fourth place, 2 points for Third Place, 3 points for Second place and 4 points for First place does not change the dominant candidate from being Candidate A but the certainty of that Candidate has decreased to 63%.

A "winner takes all" contest with no consideration of seeding, handicaps, or different points for finishes other than first, can determine dominance, but it can not determine certainty.  Before it is suggested that this is a complicated system by those who favor “winner take all of first place”, it is observed that this  is how Sports Polling, the Heisman Trophy, Hall of Fame inductions, favorite restaurants, etc. are determined.  Even in playoff systems such as the NCAA March Madness, or professional sport playoffs, seedings are used, not mere dominance. And most playoffs are series of games to increase certainty and overcome the “Any given Sunday” randomness of “Winner takes all”. Even political conventions once chose candidates based on something other than plurality takes all.  It is only in recent years in one political party that “winner takes all” state primary primaries award a state’s delegates on the basis of plurality alone.  That is a way to show dominance, but it is NOT a way to show certainty. Ranked Choice voting may sound more complicated, but it is definitely more Certain.

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