A question that has arisen* is whether fused ballots–a single vote electing president and assembly, i.e., with no opportunity for ticket-splitting–suppress the number of parties, particularly when the president is elected by plurality and assembly by PR.
A challenge in addressing this question is that fused ballots are rather rare. Moreover, they may be adopted/abolished by ruling parties/coalitions based on expectations of advantage. In other words, the direction of causality between party-system outputs and rules is more ambiguous than usual. With such caveats reiterated, here is what I find.
This is for pure presidential systems, only because I am not aware of cases of semi-presidential systems that fuse presidential and assembly votes. (In parliamentary systems, the option does not arise, or in a sense the vote is always fused. I did not include the brief case in Israel of separate and direct election of an executive who was still responsible to the parliamentary majority.)
My outcome of interest is the ratio of expected effective number of seat-winning parties (NS) or seat share of the largest party (s1) to the expectation, given the seat product of the assembly (first chamber) electoral system.
For NS, the ratio in non-fused cases is 1.13, for fused it is 0.927. This looks like good news for the hypothesis that fused ballots restrict party systems more than the separate vote does. However, the difference is not close to significant (p=0.12).
For s1, the ratio in non-fused is 1.012, and in fused it is 1.047. Obviously that’s not significant. (Also, the seat product model is pretty good–even for presidential systems!)
Note that for NS, the mean assembly party system in a presidential democracy tends to be more fragmented than expected from its electoral system. Probably not what most people expect. Perhaps this is driven by the unusually fragmented case of Brazil. If I take it out, the ratios in non-fused are 1.083 for Ns and 1.031 for s1. So not much impact.
Perhaps one should drop Uruguay from the set of fused cases. Not because ballots are not clearly fused, but because the electoral system is so different. Before 1999, parties could present multiple presidential candidates (and pool votes at party level for determining which party would win), and since then the fused ballot is only for the first round of a two-round presidential election. However, if we do this, we have only four cases left, so it is kind of meaningless. For the record, we would then have about a p=0.1 signifiant result in the expected direction. But I would put no stock in a result comparing four elections (in two countries) in one group to over 150 in the other group!
This is the list of cases with fused ballots that I am using. If I missed some, please let me know. (Angola, the case that prompted me to investigate this, is not in the dataset, nor are other countries that are not generally classified as democratic.)
country year Dominican Rep 1978 Honduras 1993 Honduras 1997 Honduras 2001 Uruguay 1989 Uruguay 1994 Uruguay 1999 Uruguay 2004 Uruguay 2009 Uruguay 2014 Uruguay 2019
To this list could be added Bolivia. However, I did not include it because elections for president were not direct before 2005 (congress chose from top three if the popular vote did not yield a majority) and since 1997 the fusion has been only between the presidential vote and the party list vote of an MMP system.
(* A version of this text was originally posted as a comment in a thread on Angola, but it seemed to warrant a place in the center row of the virtual orchard.)