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.

Empirical social choice - special issue of "Public Choice"

Does modern democracy produce outcomes preferred by a majority of the voters? One would think that this must be so.

But not necessarily.  Since the 1950s social scientists have been interested in those instances where there is a potential discrepancy between individual preferences and collective choices. For example, individuals are usually assumed to have "transitive" preferences; say, I like foie gras more than pasta and pasta more than shrimps--therefore we may assume that I like foie gras more than shrimps.  If I do not, then most people would find my ordering somewhat odd.

But when more than two such individual preferences over more than two alternatives are aggregated as a social choice (e.g. through a vote), we may get "intransitive" collective preferences--e.g.,

foie gras > pasta > shrimps > foie gras.

This "voting paradox"--most famously developed by Condorcet and in modern days applied by Kenneth Arrow and William H. Riker--has profound implications for how we may view not only democratic decisions but politics in general.  Alas, while thousands and thousands of studies have been made of the theoretical aspects of such phenomena, the empirical side is much less studied.

Since the late 1990s a large part of my own research agenda has been devoted to such issues (e.g., cycles in voter preferences [paper here], voting paradoxes in proportional electoral systems [gated paper here] and election inversions [gated paper here; ungated version here]).  The most recent issue of "Public Choice" is a special issue on "Empirical Social Choice", guest edited by myself and--on the occasion of the 30th anniversary of William H. Riker's seminal book "Liberalism against Populism" (1982)--devoted to empirical studies of voting paradoxes and the effects of different voting methods.

I have two papers in the special issue myself: 1) An general introduction devoted to Riker's book and its implications, as well as an overview of the contributions to the special issue ("Empirical social choice: An introduction", gated paper here; ungated version here); 2) an analysis of the 1975 government formation in Denmark ("Picking a loser?", gated paper here; ungated version here).  In the latter I argue that the process made visible a flaw in the Danish procedures: Given the preferences of the political parties and the system of "negative parliamentarism", the Danish political system ended up with what was possibly only the third ranked government alternative, one supported only by a minority in parliament.  Different procedures might well have produced what was the majority preferred outcome: A centre-right government led by Poul Hartling.

The special issue contains a number of interesting contributions by prominent political scientists and economists such as John Aldrich, Steven Brams, Josep Colomer, Keith Dougherty, Bernard Grofman, Nicholas Miller, Michael Munger, Mogens N. Pedersen, Bjørn Erik Rasch, Norman Schofield, Nic Tideman and Ad Van Deemen.

Do Danish voters get the government a majority prefer?

I have a new working paper out (in a preliminary version), dealing with "election inversions" in Danish elections/government formations. That is: Do Danish voters get the government(-coalition) a majority wants? One would think so, but I show that there are (at least) two types of voting paradoxes that may manifest themselves and lead to election inversions, where a majority of the voters vote for parties supporting one government, but where the other side wins. I show that

New article on voting paradoxes

My most recent, published English-language academic article is this one, in Scandinavian Political Studies, dealing with the possible occurrence of "voting paradoxes" in Danish parliamentary elections. In many ways that study began with a much earlier finding of a "Condorcet cycle" in Danish voter preferences in this 2001-article.