Wednesday, February 3, 2016

Iowa Caucus Coin Toss Math

The 2016 Iowa Caucuses had a fantastic photo finish.on Monday night with Hillary Clinton outlasting Bernie Sanders by 4 delegates to the states county conventions.  The delegates to the county conventions are allocated to the candidates based on the percentage of the caucus goers supporting a viable candidate.  A candidate is viable is he or she has more than 15% of the caucus goers present.  In the caucus room there is a scramble for unviable candidates caucus goers (in this case Martin O'Malley and uncommitted supporters) too go into either Clinton or Sanders corner.

For caucuses the networks do entrance polls of caucus goers rather than exit polls for primary and general elections.  The entrance poll tells us about who the goers are and what they were thinking as they enter the caucus room with a random sample of 1660 out of over 100,000 total goers.  The table below shows the breakdown of democratic caucus goers by gender.  Multiplying the marginal percentages for gender by the cell percentages for the candidates and then summing across columns gives the preferences of goers as they entered the room.  For example the overall % for Sanders is found by the formula 0.50*0.43 + 0.42*0.57 = 0.4544 or 45.44%.  The final delegate total suggests that the Sanders people did a better job attracting O'Malley and uncommitted caucus goers into their corner than Clinton once they were in the room.  The rest of the exit poll shows that Sanders was preferred overwhelmingly by younger goers, by those with some college or a college degree, by single goers, and by low income caucus goers.

 Candidate Men (43%) Women (57%) % Caucus Goers on Entrance Final Delegates (%) 44% 53% 49.13% 701 (49.86%) 3% 3% 3.00% 8 (0.6%) 50% 42% 45.44% 697 (49.57%) Uncommitted 3% 2% 2.43% 0 (0%)

In cases where there was a tie in the caucus room, the winner is determined by a coin toss.  For example in the case of a tie for a room with 5 delegates, 2 delegates would be awarded to Sanders, 2 to Clinton, and the 5th delegate awarded to a candidate by a coin toss.  On Monday night there were 6 caucus rooms decided by a coin toss with all 6 delegates being awarded to Clinton.  Given that the margin of victory was 4 delegates for Clinton it seems that that is what determined the outcome.  The Nightly Show with Larry Wilmore had a funny take on this.
 Who wins this coin toss?
What exactly is the probability of Clinton winning all six tosses given that a fair coin is usedWhen a fair coin is used the probability of winning one toss is 1/2 or 50%.  The chance of winning two tosses is 1/4 or 25%.  In the case of 6 coin tosses, the chance of Clinton winning all 6 tosses is 1/64 or 1.6%.  This outcome is possible by pure chance but its likelihood is very small.

**Update**
NPR has reported that there were in fact a dozen coin tosses and that Bernie Sanders won "a handful" of them according to an unnamed Democratic party official.  How many is a handful?  Can this number be independently verified?  Truth is a slippery thing indeed.  There is apparently this one video where Sander's did win a coin toss so he has won at least one toss.

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