It is surprising just how challenging it can be to answer the question, how many parties are there in an election? Of course, it was precisely because counting parties is not actually straightforward that the “effective” number of parties was devised (Laakso and Taagepera, 1979). It is a size-weighted count, and a valuable index of party-system fragmentation.
However, sometimes we might actually want a more “raw” count. It may be of limited utility to use a straight count that takes the party with one seat to be equivalent to the party that won more than half, yet even limited utility is utility. For instance, in building the models in Shugart and Taagepera (2017), Votes from Seats, we often needed to resort to “actual number of seat-winning parties” even if only as one step towards some broader model-building goal. (For vote-earners it is even harder, so we rely on a phantom quantity, the “number of pertinent vote-earning parties”.)
It might seem that counting how many parties won seats would be pretty straightforward. And, yes, of course, it is! Just count how many have at least one seat. However, if one wants to use this number to build further, it might be a dead-end. For instance, if we are trying to determine how many “serious” parties there are (and this is not the same thing as the “effective” number) we probably want to eliminate some very minor parties even if they have a seat.
We would not want, for example, to count every independent as a “party” if we were trying to count parties in a meaningful sense of the latter term. And we certainly do not want to aggregate all independents as if they were collectively a single party. An independent, by definition, is running on his or her own efforts and in one district. So an independent is not a party any more than the entire collection of independents is a party.
And then there are regional parties. Clearly they matter, and can even be very important in some countries. Right now in the UK, one of them is needed to give the government a majority in the House of Commons. And the parliament of India is full of them. So is Spain’s, and recent events remind us that regional politics really is a thing in Spain.
A related complication arises when some “national” party is in some sense an alliance of many parties that use distinct labels (and maybe have distinct local alliance partners) in different electoral districts or clusters of districts. Again, Spain is such a case. The “United Left” is anything but, as it operates under different local labels and alliances in different regions. Yet most sources would say it is one party at the national level. Perhaps it is, but then we may be losing something of value about Spanish politics if we ignore the fact that the “party” is presenting a different name to voters in different places.
I will not be proposing a specific solution here, but I wanted to determine how different standards of what to count make a difference to the number we end up.
I will set a series of standards for how “serious” a party needs to be. The most lax one is simply to count any label under which at least one candidate was elected. This approach means counting each independent as a “party” and it also means counting any alliance in one district that has even a slightly different label or combine of parties than in another district as a distinct party. (Immediate issue: the method may not recognize where the “same” party/alliance presents its name under a different local language. Maybe that’s not actually an issue, or maybe it is.)
We can then go one step towards a more restrictive count by dropping any party that ran only in the district in which it won. This standard obviously drops all independents.
Next steps towards more restrictions in what counts as a “party” take some exponent on the total number of districts, and say a party must have run in that number to be counted. For example, it must have run in a number of districts equal to the square root of the total number of electoral districts (E). Or it must have run in E^.75 or E^.975, or whatever. Any such cutoff is obviously arbitrary. I rather like E^.975 for defining “national” parties because it means almost every district without “penalizing” a party that does not run in a few districts. For instance, in the UK 2010 it means 553 districts and in the US it means 374. But in a country with few districts, it imposes the requirement that the party run everywhere (Luxembourg has only four districts, and 4^.975 is still 4 when we round up). For most purposes, however, this is much too strict a way to count “how many parties there are”. We can use E^.75, which works out to nearly half in the US and UK, but still almost all districts in countries with few districts (like many PR countries, as well as small island states).
Of course, E^.75 will cut out parties that sure seem to matter, like the SNP in the UK. There’s no good answer!
(Why not use some fraction of the districts? Because sometimes there is just one district, and an exponent does not run into the problem of allowing the number of districts to count as serious to be less than one.)
So let’s see what difference it makes. The table below (which I know exceeds the template’s parameters!) gives the counts via different measures from some recent elections, but I will pull out a few to discuss.
If we use all seat-winning lists in Brazil, we get around 100! That’s because parties appear in different alliances in every state, and so every district-list that wins a seat gets counted as a separate party. If we use the E^.75 standard, we are down to no parties! Not good. (By way of comparison, counts based on national reports of election results would yield 18 to 22 parties in recent Brazilian elections. But these counts include the component parties, not accounting for the various state-level alliance lists in which most of the seats are won. So really they are counting something different, and it is not clear which is correct. A similar situation arises in Finland, albeit less drastically. See the note and links at the bottom of the table.)
Somewhat more practically, take the case of India in 1999. Counting all seat-winners gives us 44, which is rather absurd. But as soon as we drop all those who ran only in the district where they won, we are down to 31. That is valuable information because it tells us that several of these “parties” have no plausible impact on the national party system (unless of course their one seat becomes pivotal in the assembly). If we cut it to E^.5, we are left with 15. Still a lot of parties, but it really underscores how many of these parties have only a token presence in vote-earning outside the places they win. Even at E^.75, the Indian count seems reasonable as a rough approximation of “national” partes (5). The other cutoffs clearly bite too hard. (In India, knowing only the electoral system, we would expect around five parties, because the seat product (543) raised to 1/4 gives us 4.83. We show in Votes from Seats that this formula is very accurate for most elections in a worldwide dataset. We also show that if the many Indian regional parties with seats are counted according to their national alliances, the seat product correctly estimates the effective number of components (alliances rather than parties); I do not know what the raw count of the number of seat-winning alliances is, but about five would be close.)
How about the UK? We start with 11 seat-winners in 2010; dropping those that run only in one district still leaves us with 10. Yes, the UK is pretty fragmented, after the big parties! The square-root standard leaves six, which is probably a reasonable count. (By the seat product, we’d expect 5.) Let’s see, we have Conservatives, Labour, Liberal Democrat, Scottish National, Plaid Cymru, and pick your favorite Northern Ireland party. Even if we go all the way to E^.975, we still have three, which is sensible. If anyone asks me which are the “national” parties in the UK, I will say Conservatives, Labour, and Liberal Democrat. Full stop.
Now look at Spain. Here it is not so helpful, but it again highlights something salient about the country’s politics–just how regional it is. In 2011, we have 24 “parties” winning at least one seat. That is almost one for every two districts (there are 52). Twenty of these remain if we drop those that run only in one district. Clearly E^.975 fails to reflect that there are at the very least two “national” parties in Spain (PP and PSOE); it counts only one. But at E^.9 we get three, which is more like it for pre-2016 elections (and we get 3 also at E^.75). (For whatever it is worth, a count based on the nationwide reporting of parties–for which something like the United Left gets counted as one party–results in 13 seat-winning parties in Spain in 2011.)
The table also includes counts of how many parties run, whether or not they win, at the various standards other than the rather useless one of anyone appearing on a ballot or getting a vote. Check out Albania! Even the US sometimes has more than ten parties running in 21 or more districts and Canada has a similar number running in 17 or more.
The bottom line is that counting parties is less straightforward than it might seem. If we need a relatively raw count, rather than the effective number (or some other index) then we need some standard of what “counts” as a party. It may not be every one that has one seat, just like it surely is not every one that appears on a ballot or wins a vote. Different standards might be useful for different purposes, but one needs to be careful so as not to pick a standard because it gives the count one wants. That is, there needs to be a scientific purpose behind the selected standard.
|Country||Year||E (no. districts)||no. seat-winners||no. seat-winners running E>1||no. seat-winners running E^.5||no. seat-winners running E^.75||no. seat-winners running E^.9||no. seat-winners running E^.975||no. running in E^.5 districts||no. running in E^.75 districts||no. running in E^.9 districts||no. running in E^.975 districts|
Note: There a country has “_a” after its name it indicates that the counts are based on alliance lists, not the individual parties that comprise the list. I have discussed this issue before (e.g., on Brazil, Chile and in a comparison of Brazil and Finland.
Data source: This information is all extracted from the Belden and Shugart dataset acknowledged in Votes from Seats. Much of the original data comes from the Constituency Level Electoral Archive, although some of it we collected ourselves.