Voting paradoxes in the 2016 Republican presidential primaries

My social choice analysis of "voting paradoxes" in the 2016 Republican presidential primaries (Trump, Condorcet and Borda: Voting paradoxes in the 2016 Republican presidential primaries) has now been published in the European Journal of Political Economy.  Here is the abstract:

"The organization of US presidential elections makes them potentially vulnerable to the “voting paradoxes” identified by social choice theorists but rarely documented in real-world elections. Using polling data from the 2016 Republican presidential primaries we identify two possible cases: Early in the pre-primary (2015) a cyclical majority may have existed in Republican voters’ preferences between Bush, Cruz and Walker. Furthermore, later polling data (January-March 2016) suggests that while Trump (who achieved less than 50% of the total Republican primary vote) was the Plurality Winner, he could have been beaten in pairwise contests by at least one other candidate and may have been the Condorcet Loser. The cases confirm the empirical relevance of the theoretical voting paradoxes and the importance of voting procedures."

Social choice and the 2016 US presidential election

Marquis de Condorcet

This is one of those "seasons" of the US political cycle, where I follow US opinion polls very closely, and I noticed a funny, little odd thing looking at some of the polls--specifically the RealClearPolitics.com polling averages (General Election head-to-head match-up polls & national party primary polls of Democrats and Republicans) and a single head-to-head match-up primary poll (with Cruz v. Trump and Rubio v. Trump, NBCNews/WSJ) not included in those averages.

On the day of the Iowa Caucus I wrote a hasty little research note on the topic, which you can download here.

But here is the gist of it, where > means "beats":

• Clinton > Trump
• Clinton > Sanders
• Cruz > Clinton
• Rubio > Clinton
• Rubio > Sanders
• Sanders > Cruz
• Sanders > Trump
• Trump > Cruz
• Trump > Rubio

If that is correct (and we are disregarding the question of the confidence intervals of the polls), then we would seem to have three possible "cyclical majorities" (of a sort) involving all five leading contenders for the nomination of the two parties:

• Sanders > Trump > Rubio > Sanders 
• Rubio > Clinton > Trump > Rubio 
• Cruz > Clinton > Sanders > Cruz 

Not Marquis de Condorcet

This is, of course, somewhat speculative and quite counter-factual, given that it is based in different "constituencies" (so to speak).  But it certainly suggests--as in the "Condorcet Paradox"--that no matter which of these five might win the US presidential election in November, there is a non-trivial possibility that that person could be beaten in a pairwise contest by at least one other candidate.