Italy 2018: Assessing the electoral-system effect

[Note: data calculations in this post are based on preliminary results. For some updated information, see the comments by Manuel below.]

The Italian election of 4 March produced an “inconclusive” result, as the media (at least English-language) are fond of saying when no party wins a majority. However, there are many aspects of the Italian result that are being reported with considerable confusion over how the electoral system works. In this post, I want to try to offer a corrective, based on the results published in La Repubblica.

These summaries will apply to the Chamber of Deputies only. The interested reader is invited to perform the equivalent calculations on the Senate and report them to the rest of us.

One common note of confusion I have seen in media accounts is insufficient clarity about the distinction between alliance (or “coalition”) and party. The design of the electoral system is fundamentally one that works on pre-election alliances, each consisting of one or more parties. Obviously, if an “alliance” consists of only one party, it is just that–a party. Rather than invent some encompassing term, I will use “alliance” when referring to the set of vote-earning entities (that would be a “more encompassing term”!) that includes pre-electoral coalitions, and “party” only when looking at the sub-alliance vote-earning entities. In the case of the Five State Movement (M5S), the “alliance” and “party” are the same thing. In the case of the other two main entities, they are different. Centrodestra (Center-right, or CDX) is a pre-electoral alliance consisting of the Lega, Forza Italia, and other parties. Centrosinistra (Center-left or CSX) is a pre-electoral alliance consisting of the Democrats (PD) and other parties.

No alliance has achieved a majority of seats. The M5S is the biggest party, while the CDX is the biggest alliance. As the table below shows, CDX leads with 263 seats, with M5S second on 222. The CSX has 118.

The breakdown is as follows, showing the three main alliances, plus a fourth one, Liberi e Uguale, which was the only other to clear the 3% threshold for individual parties or 10% for multiparty alliances:

Alliance % votes seats % seats
Centrodestra 37.0 263 42.5
M5S 32.7 222 35.9
Centrosinistra 22.8 118 19.1
Liberi e uguali 3.4 14 2.3
others 4.1 2 0.3

(There are two other seats indicated as being won by “Maie” [Associative Movement Italians Abroad] and “Usei” [South American Union Italian Emigrants]; no vote totals are given.)

The total comes to 619. Another summation from the same sources yields 620. I will not worry about the small discrepancy.

As an aside, I have seen at least two accounts of the result that have had phrasing referring to no party having won the 40% “required” to form a majority. There is no such requirement. It is true that no alliance or party attained 40% of the overall votes cast. However, the understanding that some authors (even one Italian political scientist writing on a UK blog) seem to have is that had someone cleared 40%, that alliance or party would have been assured of a majority of seats. That is incorrect. In fact, given the way the system is designed (more below), it is highly unlikely that an alliance with just over 40% could have won more than half the seats. Possible, but very unlikely (and we might say not significantly less likely had it won 39.99%). This “40%” idea floating around is just totally wrong.

The presentation of the overall result leads me to a second key point: the outcome is not terribly disproportional. However, it would be wrong to conclude from this observation that the electoral system was “proportional”. It is not designed to be such, and the disproportional elements of the design have significant consequences that I shall explain.

In terms of the Gallagher index of disproportionality (D), the result, based on alliances, yields D=5.40%. That is slightly greater than the median for my set of over 900 elections, and somewhat less than the mean of the same set (4.9 and 7.1, respectively). It is very slightly greater than the mean for PR systems (4.6; median 3.8).

Thus, based on the outcome measure of disproportionality, the Italian system looks like a moderately disproportional variant of PR. however, it is not a PR system! We do not ordinarily classify electoral systems based on their outputs, but on their rules. By that common standard, the Italian system is not PR, it is mixed-member majoritarian (MMM). It consists of two components–one that is nominal and the other than is list. The nominal component is plurality rule in single-seat districts, while the list component is nationwide PR (for alliances or parties that clear the threshold). Crucially the list seats are not allocated in compensatory fashion, but in parallel; this is the feature that makes it MMM, not MMP.

Unusually for MMM, but not disqualifying it from that category, the list-PR component is a good deal larger than the nominal (plurality) component. The nominal component is only around 35% of the total. However, the lack of compensation means that any alliance (or party) that can win pluralities in a substantial number of single-seat districts (SSDs) will be over-represented even after adding on all those list-PR seats. And such over-representation is precisely what happened.

If we look at the 398 list-PR seats and their allocation to parties (and here I do mean parties), we see a substantially more proportional output than overall. The Gallagher index is D=3.93%. This is, as reported above, right near the mean and median for pure PR systems. Just as we would expect! And most of the disproportionality comes from parties below the threshold, not from disparities among the over-threshold alliances. Around 4% of the vote was cast for alliances (or individual parties) that did not qualify for any seats. Some other votes are lost due to a provision that sub-alliance parties that get under 1% of the vote also have their votes wasted. If a party is between 1% and 3%, its votes are still credited to the alliance of which it is a part, even though such a party is barred from winning any seats in the list component.

Focusing on some of the major parties, we see that the major CDX partners were not much over-represented in the list component of the system: Lega has 17.4% of the vote and 73 seats (18.3%) for an advantage ratio (%seats/%votes) of A=1.05. Forza Italia has 14% of votes and 59 seats (14.8%) for A=1.06. The second largest alliance, the stand-alone party M5S has 32.7% of votes and 33.7% of seats for A=1.03. In the CSX, the PD is more over-represented, with 18.7% of the votes but 91 seats (22.9%), and A=1.22. I suppose this is because its partners mostly failed to qualify for seats, but the votes still get credited to the alliance (as explained above), and hence to the PD.

We see from these results that, with the partial exception of the PD, the parties are represented quite proportionally in the list-PR component of the MMM system. What gets us from D=3.93% in the list component to D=5.40% overall is precisely the fact that the nominal tier of SSDs exists and favored, as one would expect, the larger alliances. The following tables shows just how dramatic this was.

Nominal result
seats % seats % votes
Centrodestra 109 49.1 37.0
Centrosinistra 24 10.8 22.8
M5S 89 40.1 32.7
total 222 100.0

The vote percentages are the same as those shown in the first table, because there is no ticket-splitting between the two components. Each alliance presents a single candidate in each district, and the voter can vote for either a party list or an alliance candidate. Votes for a list are attributed to the candidate, and a vote for the candidate is proportionally divided among the lists in the alliance that nominated the candidate (with the previously noted caveat about parties whose national vote is in the 1-3% range).

The seats in the nominal component are distributed quite disproportionally: the largest alliance, CDX has nearly half of them, despite only 37% of the vote. The M5S is also over-represented, with about 40% of seats on just under a third of the votes. As is typical under SSDs with plurality, the third-place finisher, CSX, is significantly underrepresented, with a percentage of seats not even half its votes percentage.

Also as is typical, candidates often won their district seats on vote percentages in the low 40s or less. The mean district winner had 43.9% of the vote. For the M5S the mean was 45.4%, while for CDX it was 43.7%. As might be expected for a third force winning some seats, the CSX tended to benefit most of all from fragmented competition, with its mean winner having 39.2%. The lowest percentage for any SSD winner was 24.1% (M5S in Valle d’Aosta). Four winners had over 60%, including two from M5S and two from CSX; the maximum was 65% (CSX in Trentino-Alto Adige/Südtirol).

The media focus is on the “inconclusive” result, and many are blaming “PR” and the failure of any party (or alliance) to reach 40% of the votes for the lack of a “clear” verdict. However, we have seen here that the system is not proportional, even if the overall level of disproportionality is modest. If the entire system had been based on the allocation used in the list-PR component, we would be looking at CDX with 38.7% of seats, M5S with 33.7%, and CSX with 23.6%. However, given the actual MMM system, and its inherent disproportionality, the result is CDX 42.5%, M5S 35.9%, and CSX 19.1%. The non-PR aspect of the system thus has made a difference to the seat balance. The bargaining context would be difficult either way, but the two largest alliances are both boosted somewhat by features of the electoral system. Had the leader reached 40%, it would have netted only slightly more seats, surely still short of a majority, because–contrary to some claims circulating–there was no guarantee of a seat majority for reaching any given vote percentage. To form a majority of parliament, an alliance would have to win a very large percentage of the single-seat districts as well as some substantial percentage of the votes (probably a good deal higher than 40%). That the outcome is “inconclusive” says more about the divisions of the Italian electorate than it does about the supposed problems of a proportional system that Italy doesn’t actually have.

Thank you to Gianluca Passrrelli for sharing the link from which I based my calculations and for his excellent chapter in the forthcoming Oxford Handbook of Electoral Systems.

El Salvador ballots

Thanks to the really wonderful Twitter feed of La Prensa Grafica, following are some photos of voted ballots from El Salvador’s assembly elections of 4 March.

The ballot format is “free list” under which it is a party-list proportional-representation system, but unlike other types of list, the voter can give preference votes to candidates nominated on different lists (a feature sometimes known as panachage).

Here is one that is marked for candidates in several different lists, but none in the government-supporting parties, FMLN (red) and GANA (orange).

Here is one that marked all of the candidates in the ARENA party.

That’s a lot of work! A voter who wants to vote a straight ticket can simply put an X over the party symbol at the top, and it counts the same as a vote for each candidate on the list.

Now here is one whose vote will count for no one, but the voter had fun making statements.

Under the free-list system, a party’s votes is the sum of all the preference votes its candidates receive (including the label votes counted as one for each candidate on the list). Any preference vote thus contributes to the list’s pooled vote total for purposes of calculating seats per list. If a voter does not cast all M votes (where M is the district magnitude), that voter is sacrificing a percentage of his or her entitled voting weight.

This process also means that calculating national party vote totals is not straightforward. I am not sure what method of weighting votes across the varying-magnitude districts is used in El Salvador’s official reporting of national totals.

Italy, 2018

It is 4 March, and in addition to El Salvador, Italy has its election today.

It is especially interesting in that it is the first election under (yet again) a new electoral system. This system is MMM, although quite different from the MMM system in place for a few elections in the 1990s and early 2000s. Details of the system were discussed in an earlier thread. I offer this one for further discussion, in particular of the results as they come in.

Lebanon’s New PR Electoral System: Undermining Proportional Outcomes in a Proportional Representation Electoral System

This is a guest post by Amal Hamdan

In May 2018, parliamentary elections are scheduled to be held in Lebanon using a PR electoral system for the first time. The last parliamentary elections in Lebanon were held in June 2009. Since then, parliament has extended its own term twice. After years of deadlock over electoral reform, Lebanon’s two main rival political alliances, the March 14 and March 8 blocs, passed a law in June 2017 abolishing the Block Vote [MNTV–ed.] electoral system, used since 1958 for legislative elections, and introduced Open List Proportional Representation (PR) (Law No.44). An analysis of key technical aspects of the new law – namely, the formula used to distribute seats to lists and an informal threshold for list eligibility – suggests that it was designed to enhance the chances of candidates within the March 14 and March 8 blocs to be elected and diminish the possibility of electing candidates outside these alliances. Lebanon has been politically polarized between the March 14 and March 8 blocs since 2005, following the assassination of former Prime Minister Rafic Hariri which led to an end of Syria’s hegemonic grip over Lebanese politics. The main political factions comprising the March 14 alliance are the Future Movement (FM), the Sunni community’s main political representative; Maronite Christian Samir Geagea’s Lebanese Forces (LF); and the Christian Kataeb party. The March 8 bloc comprises the main Shia political parties, Hizballah and the Amal Movement and their mainly Maronite Christian ally, the Free Patriotic Movement. Until 2009 Druze leader Walid Joumblatt’s Progressive Socialist Party (PSP) was also part of the March 14 bloc but has since withdrawn, further reinforcing Joumblatt’s ability to play political kingmaker in Lebanese politics.

128 parliamentarians will be elected in 15 new ‘major’ electoral districts. Many, but not all, of these 15 districts are comprised of minor constituencies [qada]. Each voter casts a ballot for a list of candidates; voters have the option to cast one preferential vote for their favorite candidate, as long as the candidate is on the same list they have chosen. There is a key restriction on candidates’ preferential vote: if the major electoral district is comprised of more than one minor constituency, voters can use their preferential vote only for candidates within their minor constituency, and not any candidate in the major electoral district.

The new electoral law adopts the Hare Quota Largest Remainder (HQLR) formula to distribute seats to lists. Under the HQLR, the ‘price’ of a seat, in the currency of votes, is determined by dividing the total valid votes cast in a district by district magnitude (number of seats allocated in the district). This provides the quota or price of a seat. Under Lebanon’s PR system, for every whole quota a list has won, it receives a seat. If there are unfilled seats, they are allocated to lists with the largest remaining votes.

Only lists that receive one full whole quota are eligible to seat allocation; any lists that receive less than 1.00 or a full simple whole number are disqualified. One full whole quota or the threshold for lists to qualify for seat allocation varies across districts from 7.69% of votes (Mount Lebanon 4) to 20% (South Lebanon One). Table 1.1 identifies the major constituencies and the effective threshold in each district for lists to qualify for seat allocation. The minor constituencies or qada within each major district are in brackets.

Table 1.1

Major Constituency Effective Threshold of List Votes
South Lebanon One (Sidon; Jezzine) 20%
Beqaa Two (Rashaya; West Beqaa) 16.67%
Mount Lebanon Three (Baabda) 16.67%
South Lebanon Two (Tyre; Zahrani) 14.29%
Beqaa One (Zahle) 14.29%
North Lebanon One (Akkar) 14.29%
Beirut One 12.50%
Mount Lebanon One (Jbeil; Kesrewan) 12.50%
Mount Lebanon Two (Metn) 12.50%
Beqaa Three (Baalbeck-Hermel) 10.00%
North Lebanon Three (Zgharta; Bcharri; Koura; Batroun) 10.00%
Beirut Two 9.09%
South Lebanon Three (Bint Jbeil; Nabatieh; Marjayoun-Hasbaya) 9.09%
North Lebanon Two (Tripoli; Minnieh-Dinnieh) 9.09%
Mount Lebanon Four (Chouf; Aley) 7.69%


Besides the threshold, an additional provision in Lebanon’s PR electoral law favors well-established alliances such as the March 14 and March 8 blocs and strongly reduces opportunities for less established, smaller parties or electoral alliances from winning seats.  Under the new law, the Hare quota will be calculated a second time excluding the votes won by a list or lists that did not achieve the electoral quotient. A hypothetical example of three lists competing in the newly-created South Lebanon One constituency, which has a total of five seats allocated to its minor constituencies, Sidon and Jezzine, demonstrates how provisions in Lebanon’s PR electoral law decreases chances of candidates not running on major ballots from winning. The following table provides seat and confessional allocation in South Lebanon One:

South Lebanon One ‘Major’ Constituency
Minor Constituency (Qada) No. Seats and Confessions
Sidon Qada 2 Sunni
Total Seats in Sidon Minor District 2
Jezzine Qada 2 Maronite
1 Greek Catholic
Total Seats in Jezzine Minor District 3
Total Seats in South Lebanon One 5

To calculate the threshold for a list to qualify for seat allocation, the total number of valid votes cast for all lists in the South One district are combined and divided by district magnitude. Assume there are three hypothetical lists competing in the South Lebanon One district. The number in the brackets next to each candidate indicates the candidate’s preferential votes.

Lists Contested in South Lebanon One Major Constituency
Minor Constituency and Confession List A List B List C
Sidon Qada      
Confessional Seat Sunni A1 (25,460) Sunni B1 (13,512) Sunni C1 (7,543)
Confessional Seat Sunni A2 (23,041) Sunni B2 (5,266) Sunni C2 (4,289)
Jezzine Qada
Confessional Seat Maronite A3 (10,792) Maronite B3 (15,648) Maronite C3 (7,399)
Confessional Seat Maronite A4 (5,403) Maronite B4 (13,285) Maronite C4 (4,338)
Confessional Seat Greek Catholic A5 (5,220) Greek Catholic B5


Greek Catholic C5


List’s Total Votes 73,917 64,826 33,168

Note: The total votes won by each list exceeds its total preferential votes because voters have the option of voting for the list without casting a preferential vote for a candidate (Article 98, Clause 1)


The first step is to calculate whether lists are eligible to qualify for seat distribution; only those with at least one whole quotient will be eligible.

Step 1. Calculate the electoral quotient:

Electoral Quotient: (73,917 List A votes + 64,826 List B votes + 33,168 List C votes) = 171,911 ÷ 5 seats = 34, 382

Step 2. Calculate if lists won a whole quotient by dividing each list’s total votes by the electoral quotient:

List A: 73,917 list votes ÷ 34, 382 electoral quotient = 2.15.

List B: 64,826 list votes ÷ 34, 382 electoral quotient = 1.88.

List C: 33,168 list votes ÷ 34, 382 electoral quotient = 0.96.

Since List C won less than one whole electoral quotient it is disqualified – even though this list won 19.29% of total votes cast. Since a list has been disqualified, a second electoral quotient using the HQLR formula must be calculated to distribute seats to eligible lists.

 Step 3. Calculate the second quotient:

 Formula for second quotient: Qualifying Lists’ Votes ÷ District Magnitude.

Second Quotient: (73,917 List A votes+ 64,826 List B votes) = 138,743 ÷ 5 seats = 27,749.

The price of a seat dropped from 34,382 to 27,749 votes. Arguably, the provision to calculate the price of a seat twice is aimed at lowering the cost and enhancing the March 14 and March 8’s blocs chances of sharing seats (presuming these alliances remain in tact).

Step 4. Distribute seats to qualifying lists.

This is determined by dividing the qualifying lists’ total votes by the second electoral quotient.

 List A: 73,917 ÷ 27,749 = 2.66 = 3 seats.

List B: 64,826 ÷ 27,749 = 2.33 = 2 seats.

The next step is to distribute seats to candidates. Seat distribution to candidates across lists will not be straightforward in Lebanon since PR will be implemented alongside a confessional quota. The next section demonstrates how implementing a PR electoral system alongside a confessional quota will likely lead to anomalies in seat distribution and consequently, anomalies in representation.

The Potential Anomalies in Seat Distribution under Lebanon’s PR Electoral System

Lebanon is comprised of 18 officially recognized religious communities, known in Lebanese jargon as confessions or sects. These 18 sects are mainly Muslim and Christian denominations, although there remains a small Jewish minority. None of these 18 confessions are a majority, making Lebanon a country of minorities. All 128 parliamentary seats are reserved for 10 Muslim and Christian confessional communities. One seat is reserved for ‘minorities’, meant to represent the remaining communities not designated seats.

To distribute seats to candidates in qualifying lists, each candidates’ percentage of preferential votes is calculated; then all candidates are ranked in a single list from highest to lowest percentage and seats are distributed accordingly. However – seat distribution will also need to take into account the confessional allotment of seats and their allocation to minor constituencies: if all the seats reserved for a confession have been filled, a candidate can be disqualified even if he or she is ranking higher than their opponent. A candidate may also be disqualified if all the seats allotted to their minor constituency have been filled. Drawing on the hypothetical example from the South Lebanon One district where List A won 3 seats and List B won 2 seats clarifies these points and demonstrates how potential anomalies in representation could arise in Lebanon’s new PR electoral system.

Step 1.  Calculate each candidates’ percentage of preferential votes.

This is done by dividing the number of preferential votes won by a candidate by the total preferential votes cast for all candidates, regardless their confession, from qualifying lists in each qada separately. For example, the formula to calculate candidate Sunni A1’s percentage of preferential votes in the Sidon minor constituency is calculated by dividing their preferential votes by the total preferential votes won by candidates in qualifying lists in Sidon alone, rather than the major constituency:

% of Preferential Votes: Candidate in Qada ÷ Total preferential votes for all candidates in qualifying Lists in Qada.

Sunni A’s % percentage of preferential votes: Sunni A preferential votes ÷ Total preferential votes from qualifying lists in Sidon = 25,460 ÷ 67,279 = 37.84%

The following table calculates candidate’s percentage of preferential votes in each minor constituency in the South Lebanon One electoral district.

South Lebanon One District
Minor Constituency (Qada) List A List B
  Candidate No. Preferential Votes % Preferential Votes Candidate No. Preferential Votes % Preferential Votes
Sidon Sunni A1 25,460 37.84% Sunni B1 13,512 20.10%
Sunni A2 23,041 34.25% Sunni B2 5,266 7.83%
Total Preferential Votes in Sidon Qada  




Jezzine Maronite A3 10,792 16.54% Maronite B3 15,648 23.98%
Maronite A4 5,403 8.28% Maronite B4 13,285 20.36%
Greek Catholic A5 5,220 8.00% Greek Catholic B5 14,914 22.85%
Total Preferential Votes in Jezzine Qada  




Step 2. Rank all candidates from both constituencies from the highest percentage of preferential votes to the lowest.

Candidates’ Ranking According to Percentage of Preferential Votes, South Lebanon One District
Rank Candidate Minor Constituency % Preferential Votes
1 Sunni A1 Sidon 37.84%
2 Sunni A2 Sidon 34.25%
3 Maronite B3   Jezzine 23.98%
4 Greek Catholic B5   Jezzine 22.85%
5 Maronite B4   Jezzine 20.36%
6 Sunni B1 Sidon 20.10%
7 Maronite A3   Jezzine 16.54%
8 Maronite A4   Jezzine 8.28%
9 Greek Catholic A5   Jezzine 8.00%
10 Sunni B2 Sidon 7.83%


Step 3: Distribute seats to candidates.

Seats are distributed to candidates in descending order of their percentage of preferential votes, but with these critical caveats:

  • If the seats for a confession in a minor constituency have been filled, the remaining candidates from that confession are excluded, even if they have won higher percentages of preferential votes than candidates from other confessions;
  • once the seats allocated to a list have been filled, the remaining candidates for that list are disqualified, even if they have higher percentages of preferential votes from other lists.
  • If candidates are tied for preferential votes and are both eligible because the confessional quota in their district hasn’t been filled, the older candidate wins the seat.

In the hypothetical example, the distribution of seats to candidates according to minor constituency and confessions is the following:

List A: 3 Seats List B: 2 Seats
Candidate A1 (Sunni/Sidon)  B3 (Maronite/Jezzine)
Candidate A2 (Sunni/Sidon) B5 (Greek Catholic/Jezzine)
Candidate A3 (Maronite/Jezzine)


This demonstrates exactly the potential anomalies in representation under Lebanon’s new PR system: although the candidate in rank 5, Maronite Candidate B4 won 20.36% preferential votes, he or she was disqualified because List B’s two seats had been filled and consequently, the seat was awarded to the candidate in rank 7, Maronite Candidate A3, who received 16.54% of preferential votes. The candidate in rank 6, Sunni B1, was also excluded because all the Sunni seats in Sidon were filled; even if they had not been filled, List B also already been allocated its two seats.

Summary of new Italian electoral system

If you have been unclear on what the new Italian electoral system–to be used the first time this March–really is, there is a good summary.

Broadly, it is mixed-member majoritarian (MMM, and definitely not MMP, contrary to a few claims I have seen). But with only 3/8 of the seats elected from single-seat districts, it stretches the definition at least a little bit. Anyway, the components (nominal-district and list-PR) are allocated in parallel.

There are some complicated provisions regarding the relations of votes for district candidate and lists, having to do with parties running in alliances, but there is no way to split across alliances. There is no partial compensation mechanism as there was in the MMM system (which had a balance tilted more in favor of the nominal tier) that Italy used between 1994 and 2001.

How many parties are there?

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
Albania 2009 12 6 6 6 6 6 6 34 34 34 34
Albania 2013 12 7 7 7 7 7 7 66 66 66 66
Barbados 1999 28 2 2 2 2 2 2 2 2 2 2
Barbados 2003 30 2 2 2 2 2 2 2 2 2 2
Barbados 2008 30 2 2 2 2 2 2 2 2 2 2
Brazil_a 1998 27 82 10 1 1 1 0 2 2 2 0
Brazil_a 2002 27 98 13 3 0 0 0 6 1 0 0
Brazil_a 2006 27 101 16 3 0 0 0 8 2 1 0
Brazil_a 2010 27 99 10 2 1 1 0 5 2 1 0
Canada 2000 301 5 5 5 5 4 4 11 8 4 4
Canada 2004 308 5 4 4 4 3 3 10 6 4 4
Canada 2006 308 5 4 4 4 3 3 11 5 4 4
Canada 2008 308 6 4 4 4 3 3 10 5 4 4
Canada 2011 308 5 5 5 5 4 4 9 5 4 4
Chile_a 2005 60 3 3 3 2 2 2 4 3 3 3
Colombia 2006 33 19 15 10 8 4 1 18 12 6 1
Colombia 2010 33 13 11 11 11 5 2 12 11 5 2
Colombia 2014 33 14 12 9 9 6 2 10 10 6 2
Costa Rica 1998 7 7 6 6 6 6 6 14 14 14 14
Costa Rica 2002 7 5 5 5 5 5 5 13 13 13 13
Costa Rica 2006 7 8 5 5 5 5 5 13 13 13 13
Costa Rica 2010 7 8 7 7 7 7 7 9 9 9 9
Croatia 2007 13 9 8 6 6 2 0 22 17 5 0
Czechia 2002 14 4 4 4 4 4 4 23 21 21 21
Czechia 2006 14 5 5 5 5 5 5 20 18 18 18
Dominican Rep. 1998 30 3 3 3 3 3 3 13 12 10 10
Dominican Rep. 2002 47 3 3 3 3 3 3 18 18 18 14
Dominican Rep. 2006 47 3 3 3 3 3 3 20 20 18 16
El Salvador 2006 14 5 5 5 5 5 5 5 5 5 5
El Salvador 2009 14 5 5 5 5 5 5 6 6 6 6
Finland_a 1999 15 25 6 6 5 2 0 9 7 3 0
Finland_a 2003 15 21 7 7 5 2 0 12 8 5 0
Finland_a 2007 15 20 7 6 6 2 0 14 10 5 0
Finland_a 2011 15 13 8 8 7 6 0 16 14 9 0
Ghana 2000 200 10 4 4 4 4 3 6 6 5 3
Ghana 2004 230 5 4 4 4 3 2 6 4 3 2
Honduras 2001 18 5 5 5 5 5 5 5 5 5 5
India 1998 543 45 34 14 6 2 1 18 6 2 1
India 1999 543 44 31 15 5 2 0 20 6 2 0
Israel 2003 1 13 0 13 13 13 13 27 27 27 27
Israel 2006 1 12 0 12 12 12 12 31 31 31 31
Israel 2009 1 12 0 12 12 12 12 33 33 33 33
Israel 2013 1 12 0 12 12 12 12 32 32 32 32
Jamaica 2002 60 2 2 2 2 2 2 4 3 2 2
Luxembourg 2004 4 5 5 5 5 5 5 7 6 6 6
Luxembourg 2013 4 6 6 6 6 6 6 9 9 9 9
Netherlands 2002 1 10 0 10 10 10 10 16 16 16 16
Netherlands 2003 1 9 0 9 9 9 9 19 19 19 19
Netherlands 2006 1 10 0 10 10 10 10 24 24 24 24
Netherlands 2010 1 10 0 10 10 10 10 18 18 18 18
Peru 2001 25 11 11 11 11 11 8 13 13 13 9
Peru 2006 25 7 7 7 7 7 6 24 23 19 10
Peru 2011 26 6 6 6 6 6 6 13 11 10 8
Portugal 2002 20 5 5 5 5 5 5 11 9 9 7
Portugal 2005 20 5 5 5 5 5 5 10 9 9 7
Portugal 2009 20 5 5 5 5 5 5 15 14 12 9
Portugal 2011 20 5 5 5 5 5 5 17 17 17 17
Spain 2000 52 22 18 6 3 1 1 23 10 7 3
Spain 2004 52 19 15 2 2 2 1 22 14 10 5
Spain 2008 52 16 12 3 3 3 2 31 19 11 7
Spain 2011 52 24 20 4 3 3 1 14 9 6 1
Trinidad 2000 36 3 3 2 2 2 2 2 2 2 2
Trinidad 2001 36 2 2 2 2 2 2 4 3 3 2
Trinidad 2002 36 2 2 2 2 2 2 4 3 2 2
Trinidad 2007 41 2 2 2 2 2 2 3 3 3 3
Trinidad 2010 41 4 4 3 2 1 1 4 2 1 1
UK 2001 659 10 9 5 3 3 3 12 5 4 3
UK 2005 646 12 10 6 3 3 3 12 5 4 3
UK 2010 650 11 10 6 4 3 3 12 6 4 4
US 2008 435 2 2 2 2 2 2 10 4 2 2
US 2010 435 2 2 2 2 2 2 8 4 2 2
US 2012 435 4 3 2 2 2 2 9 4 2 2
Zambia 2001 150 8 7 7 7 7 5 11 8 7 5
Zambia 2006 150 9 5 5 3 3 2 7 3 3 2

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 BrazilChile 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.



Catalonia 2017 result

(Following up on the pre-election entry, where I said the electoral system could make a difference to the result!)

If we aggregate the parties’ votes and seats in this week’s Catalan regional parliament election by pro-independence and pro-union blocks, we find the election produced a plurality reversal. That is, the pro-union parties won more votes, but the way the separate parties’ votes were translated into seats by electoral system resulted in a pro-indepdence assembly majority. The voting result between the blocs was not even very close, those opposed to independence winning by about 4.6 percentage points. This sort of thing should not happen under PR, but can happen when the system is malapportioned and the geographical distribution of party support favors the over-represented side.

I thank David Lublin for pointing this out, via an email message, the contents of which I am sharing here, with his permission.

In this first table are the votes by party and electoral district (data from El País). The main pro-separatist parties are JxC, ERC, and CUP, and these together have 70 of the 135 seats (as the second table below shows), but only 48.3% of the vote.

Barcelona 856382 615201 669108 491201 272632 141363 140786
Girona 79022 148702 87949 34898 16331 21539 11453
Lleida 40608 77695 63852 21618 9318 12052 10839
Tarragona 119870 95223 104057 51643 23443 17524 19976
CATALONIA 1095882 936821 924966 599360 321724 192478 183054

And here is a table David prepared of the same votes run through alternative electoral systems.

David looked at the outcomes considering:
(1) Malapportionment (actual system) v. Fair Apportionment;

(2) D’Hondt (actual system) v. Ste. Lague; and
(3) Four Districts (actual system) v. Single District.
As the following table reveals, the current setup greatly advantaged the pro-independence forces:


Back on 8 November, David had noted in a Monkey Cage post that the electoral system of Catalonia was “stacked” in the separatists’ favor. In that post, David said that Barcelona, which is the most pro-union of the districts, has 14 fewer deputies than it would have, based on its share of the population. (That would make its district magnitude 99! Of course, they could divide it into multiple districts.)

Manuel Alvarez-Rivera had previously noted the impact of the electoral system on the 2015 election, at which such a reversal also occurred. Manuel’s observations can be found both here at F&V and at his own blog, Electoral Panorama. The 2015 reversal was less severe than this year’s because in the earlier election the pro-union parties won the vote just 48.1% to 47.8%.

Catalonia and the rest of Spain need many things to work out their relationship (with or without separation). But one thing that clearly would help would be an electoral system for Catalonia’s own parliament that reflects how its people actually vote.