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.

29 thoughts on “Italy 2018: Assessing the electoral-system effect

  1. For a bit of perspective, under the old 1993-2005 electoral law no coalition ever won as much as two-thirds of the Senate’s single-member college seats, which served as the basis of the Chamber of Deputies single-member college seats currently in place. In fact, the largest proportion of single-member Senate seats (152 of 232, or 65.5%) was attained by Berlusconi’s House of Freedoms coalition in the 2001 general election…with 42.5% of the vote.

    This is also a good time to remember that in its early stages the late, unlamented “Porcellum” made a good job at passing for a bona fide proportional system, largely because in the first two elections under the system the winning coalition wasn’t that far removed from the 55% majority bonus threshold, resulting in comparatively modest levels of disproportionality; moreover, it should be pointed out as well that if an alliance actually reached 55% of the vote – as was the case with the 2008 Senate election in Lombardy – the system actually reverted to standard PR, albeit with fairly high thresholds. But then came the 2013 election, with the winning alliance securing the Chamber majority bonus with less than 30% of the vote, and the disproportionality shot through the roof. Likewise, the FPTP component of Rosatellum bis didn’t introduce significant proportionality distortions this time around, not only because there was a competitive three-way race, but also because of the concentration of M5S support in the south and the islands (where the party won all but three of 73 single-member college seats), and the center-left’s performance in what remained of the “red zone” (awful by historical standards but far better than in the rest of the country). However, there’s no guarantee this seemingly benign behavior will be replicated in future elections.

    By the way, speaking of M5S and the Mezzogiorno, I came across a news article on an Italian news media site which pointed out that because M5S won so many single-member mandates in that part of the country, they’re now running short of candidates to fill the PR list seats; apparently many of the party’s single-member college candidates were also PR list candidates.

    At any rate, while I agree that we shouldn’t come up with a new name for Italy’s electoral system, I thought as well that since we have not-so-grand coalition governments (even though the press infuriatingly insists on calling them “grand”), perhaps we could speak of Italy’s mixed member not-so-proportional system…

    Sorry, but I just couldn’t resist.

    But seriously, I finally managed to fully understand the process by which Chamber seats are allocated at the multi-member district level, and then at the lower-tier multi-member college level. I’ll have more to say about that later, but in the meantime suffice it to be said that the much-abused (by the English-language press) description of “complex electoral system” happens to be richly deserved in this case.


    • Interesting points. Thank you.

      I guess the name of the system actually should be “mixed-member not-so majoritarian”.

      Off topic, but Manuel, I hope the situation in PR (your island territory, not the electoral system type) has improved.


  2. “the maximum was 65% (CDX in Trentino-Alto Adige/Südtirol)”

    CDX is wrong. STV won the two most Germanophone districts with 61% and 65% (Südtirol, collegio uninominale 02 & 03 = Meran & Brixen)

    If STV is aligned with a coalition, it’s normally centre-left (as in C.U. 01 = Bolano/Bozen). But in those two safe districts, STV ran and won on its own, both coalitions had other candidates running.


    • Yes, I transcribed that incorrectly. I will change it to CSX, based on what La Repubblica says. I have another source that agrees that STV SVP was part of the CSX coalition. Perhaps that is incorrect, based on what you say. But CSX is what the data show, for whatever that might be worth.


    • STV? I have no idea what you’re referring to. But seriously, I assume you meant SVP.

      In any event, Italy’s Ministry of the Interior includes the SVP’s single-member college votes and seats within the center-left’s corresponding totals, so I don’t see why they should be treated differently, even if they ran opposite center-left candidates from the nationwide tickets.

      Incidentally, it’s been standard practice for SVP to have such arrangements in the predominantly German-speaking colleges. I can think of at least one reason behind this: in the Italian-speaking districts, it’s evident the German speakers have no issue with joining forces with the center-left, if that is what it takes to keep the center-right out. However, I suspect that probably doesn’t work the other way around: many Italian-speaking, center-left voters in the largely German-speaking colleges might be reluctant to back a candidate from an ethnic German party, and since SVP doesn’t really need their votes, the logical alternative is for the center-left to field its own candidates.


  3. The PD under Renzi proposed and passed this electoral law with the intention of harming the 5 Stars. The results seem to show that the PD itself was harmed more than the other parties and alliances. Their collapse may have been accelerated by this system?


    • I beg to differ. First, I’m of the view that Renzi’s ill-conceived and ill-fated constitutional reform set in motion a chain of events that would have led to Sunday’s election outcome irrespective of the electoral system.

      Secondly, while the Rosatellum bis electoral system did no favors to PD and the center-left, it didn’t treat them too badly either. In the PR component, PD actually benefitted from the exclusion of More Europe (+Europa) from the distribution of list seats, because their votes were still counted towards the center-left’s alliance total, and thus for all intents and purposes PD ended up with extra seats at the expense of More Europe. As for the FPTP component, it certainly under-represented the center-left, which (excluding Valle d’Aosta) will have at most 28 of 231 single-member college seats (24 declared and four leading with near-complete tallies), or 12.1% of the total. That figure is well below the alliance’s 22.9% of the vote, but the disparity could have been a lot worse and in fact it was in most of Italy outside the “red zone.” In the latter, the center-left finished second and won 16 of 40 SMC seats with 30.6% of the vote – a terrible performance in what used to be THE center-left stronghold as recently as 2013 (during the Matterellum era they won no fewer than 90% of the single-member seats in the area) – but far better than in the rest of Italy, where the center-left will end up with at most twelve seats (eight declared and four leading) of 191, or 6.3% of the total, despite polling 21.1% of the vote.

      Finally, YouTrend published in Italian a comprehensive analysis that shows that had there been no electoral reform, the distribution of Chamber seats under the previous “Consultellum” system would not have been that much different. Moreover, the article – available in Italian here points out that under the old bonus-adjusted PR system, the center-right alliance would have had a comfortable majority in the Chamber of Deputies, but the Senate would have remained under no overall control, leading to yet another impasse.

      P.S. the MakeMeAware pingback repeats the dubious (and increasingly tiresome) claim that 40% of the vote would have resulted in an overall parliamentary majority, which tarnished an otherwise fine article. I can only conclude that if there is such a thing as fake electoral system news, the 40% claim would seem to fit the bill.


  4. I am not sure my understanding is quite correct regarding how the votes for parties under 3% within an alliance work. There is one seat shown going to +Europa, which is part of the CSX. However, it has only 2.5% of the vote. There are also two seats shown for Svp-Patt, despite only 0.4%. (Referring to Chamber results.)

    How could these have won seats in the list component if they were under 3% (and one is under 1%)?

    The results also show two other parties within CSX that have votes of 0.5% and 0.6%, and no seats.


    • Another thing I do not understand: The source has a line for “Lega-Forza Italia-Fratelli d’Italia” as if it were a separate list within the CDX alliance. It is shown with 3 seats, but no votes are indicated for it.

      (Also within CDX: a list “Noi con l’italia-Udc” with 1.3% of votes and no seats; at least that result makes sense to me!)


      • I think I can clarify the doubts at hand. But first, off-topic, I suppose I shouldn’t complain too much: I have a house that’s still livable, with electricity, running water, telephone service (both landline and cellphone) and high-speed Internet, at least most of the time; the electric grid remains fragile, and I had yet another brownout at home late last night and this morning. Then again, just over ten percent of Puerto Rico is still without electricity, which means that some people have been without power for six months now (remember, we were hit not by one but two hurricanes, although the first one – Irma – was more of a glancing blow). At any rate, I cannot even begin to comprehend how could people carry on with their lives under such conditions, and in fact many have given up in despair and moved to the U.S. mainland.

        But now, back to Italy, the seat totals published by La Repubblica add up the mandates won in the expatriate constituencies to the figures for Italy proper, but not the corresponding vote totals. Also, the 619/620 seat discrepancy – which corresponds to a 222/223 seat discrepancy in the M5S seat total – is in all likelihood triggered by the exclusion or inclusion of Valle d’Aosta single seat, won by M5S with 24.1% of the vote. The reason La Repubblica doesn’t add the expatriate vote totals to the nationwide totals is because the latter figures come from the Ministry of the Interior, which reports the expatriate results separately from those of Italy proper, ostensibly because they are elected by separate rules i.e. they’re not (and haven’t been) covered by Rosatellum bis or Porcellum or Mattarellum or whatever-ellum/-illum; in turn, the results in Italy proper do not include Valle d’Aosta, which is reported separately because it only elects one deputy by FPTP; the region doesn’t and has never taken part in the distribution of PR list seats because it doesn’t have any in the first place. In addition, there are ten outstanding single-member college seats in or around Rome, not included in the aforementioned seat totals: of these, two have the center-right in the lead, while M5S and the center-left are ahead in four each; the tallies in all of these colleges are actually nearly complete (with at least 98% of polling stations reporting) so it appears unlikely they will change hands, but the decision is now in the hands of the Court of Appeals. Interestingly enough, in one of these colleges the leading candidate is none other than outgoing Prime Minister Paolo Gentiloni, who’s ahead by a sizable double digit margin with a large personal vote.

        As for the single More Europe (+Europa) seat, it comes from the expatriates’ Europe constituency, which as I just noted is not covered by the constraints of Rosatellum bis. Meanwhile, the South Tyrol People’s Party (SVP) is covered by a different rule: parties representing recognized linguistic minorities in regions with devolved government, and which have won either two single-member college seats or at least twenty percent of the vote in the region they fielded candidates are entitled to take part in the distribution of PR list seats in Italy proper; their votes also count to determine their corresponding coalition’s qualifying vote total. As it happens, SVP – which represents the German-speaking population of Bolzano/Südtirol province – won in two-single member colleges and also polled 24.2% in the region of Trentino-Alto Adige/Südtirol.

        In any event, the results published by the Ministry of the Interior can be found here. Note that the distribution of PR list seats in Italy proper (minus Valle d’Aosta) reflects an unpublished adjustment, which apportioned the votes cast for candidates only (i.e. for no specific party list) among their corresponding party lists in the ten outstanding single-member colleges; normally, this procedure is carried out when 100% of polling stations in a single-member college have been tallied.

        More later – power just went off – again…


      • Well, power came back right after I sent my last message, and in the meantime I found about the Lega-Forza Italia-Fratelli d’Italia seats: as in the case of the More Europe (+Europa) mandate, they’re expatriate constituency seats won by a joint list of the three parties in Europe, North America and South America.

        Noi con l’Italia (Us with Italy) was indeed part of the center-right alliance; even though it fell short of the three percent threshold and thus won no list seats, its votes counted towards the center-right’s qualifying total, and according to one news report, it won about fifteen seats in single-member colleges as part of the center-right alliance, in a clear example of what used to be known back in the days of Mattarellum as the “proportionalization” of FPTP.


      • Manuel, Thank you for these details and corrections. Much appreciated. I will leave the numbers in the post unchanged (unlike in my Salvadoran election post) because I do not think they affect the overall picture much. Maybe when all is settled I will post a summary with final numbers.

        Thank you also for the report on Puerto Rico.


      • You’re welcome.

        Now, I noted earlier on that I finally managed to fully understand the process by which Chamber seats are allocated at the multi-member district level, and then at the lower-tier multi-member college level. As it turns out, the procedures involved are broadly similar but not identical for the two tiers.

        Specifically, in the case of upper multi-member district tier, the distribution of Chamber seats in carried out in each district by the largest remainder method of PR among qualifying coalitions and stand-alone parties, as determined by the nationwide distribution of seats. The resulting seat distribution for all twenty-seven districts is then compared with the distribution of seats obtained on a nationwide basis. If a coalition or stand-alone party ends up with more seats than its assigned nationwide total, its excess mandates are successively deducted from those districts in which said coalition or stand-alone party was assigned seats with the lowest fractional remainders and at least one of the coalitions or stand-alone parties with a seat deficit has an unused remainder in the same district: if so, the seat is reallocated then to the coalition or stand-alone party with a seat deficit that also has the largest unused fractional remainder; otherwise the process moves on to the district with the immediately following remainder in ascending order that resulted in the allocation of an excess seat for the coalition or stand-alone party in question. When more than one coalition or stand-alone party has excess seats, the coalition or stand-alone party with the largest number of excess seats is dealt with first; in case of a tie, the coalition or stand-alone party with the largest nationwide electoral figure i.e. the qualifying vote total has precedence. In the case of the 2018 Chamber of Deputies election, only the Five Star Movement had an excess number of seats, namely four, at the expense of the Free and Equal list, which had a deficit of four seats; the center-right and center-left coalition obtained the same number of seats they had been assigned at the national level. Moreover, the four districts in which M5S was assigned seats with the lowest fractional remainders also happened to be districts in which Free and Equal had unused fractional remainders, so the seats in question were assigned to Free and Equal, thus equalizing the nationwide and district-level seat distributions.

        The described procedure was then carried out in each district for each of the coalitions among its constituent parties. In the case of the center-left coalition, only the Democratic Party (PD) and the South Tyrol People’s Party (SVP) qualified for the distribution of Chamber PR seats; since the latter ran only in Trentino-Alto Adige, in the remaining twenty-six districts all of the center-left’s list seats were assigned to PD. Meanwhile, in Trentino-Alto Adige PD and SVP-PATT were assigned one seat each, but since this would have resulted in the former receiving an extra seat at the expense of the latter – which had been allocated two seats on a nationwide basis – and since the district in question was the only one in which PD had been awarded a seat on the basis of fractional remainders, the Democratic Party mandate in that district was reassigned to SVP. Meanwhile, in the case of the center-right coalition, the initial district-level distribution of coalition seats resulted in the League having a deficit of three seats, at the expense of Forza Italia (one excess mandate) and Brothers of Italy (two excess seats); the latter’s excess mandates were reallocated first, since their number was larger than the corresponding figure for Forza Italia.

        Note that the described procedure altered neither the nationwide distribution of seats among parties nor the number of PR list seats assigned to each district at this stage; however, seat allocation procedures operating under dual constraints like these sometimes bring about decidedly strange outcomes, such as that of Molise, where the reallocation of seats resulted in Free and Equal receiving the single list seat assigned to the region, even though it finished a distant fourth there, well behind M5S and the two main coalitions.

        In any event, with Chamber seats allocated at the multi-member district level, the next step is to distribute seats within each district among its multi-member colleges, in districts with two or more such colleges. At this level the college-by-college distribution of seats is carried out by the largest remainder method of PR among qualifying parties, both stand-alone and within coalitions; note that in this case there is no prior distribution among qualifying coalitions and stand-alone parties. The resulting seat distribution for all colleges in a given district is then compared with the distribution of seats at the district level from the preceding stage. If a party ends up with more seats than its assigned district total, its excess seats are successively deducted from those colleges in which said party was assigned mandates with the lowest fractional remainders; the excess seat is reallocated then to the party with the largest seat deficit, in the college where the latter has the largest unused fractional remainder. When more than party has excess seats, the party with the largest number of surplus seats is dealt with first; in case of a tie, the party holding the excess seat with the smallest fractional remainder has precedence. Also, in case of a seat deficit tie, the party that has the largest unused fractional remainder comes first. Note that unlike in the case of the multi-member districts, this procedure can alter the number of PR list seats initially assigned to a multi-member college. For example, in Emilia-Romagna, multi-member colleges 1, 2, 3 and 4 started with seven, seven, six and eight seats, respectively, but in the end those figures changed to six, seven, six and nine mandates.

        Finally, the Senate has a simpler system, inasmuch as there is no nationwide seat allocation tier: list seats are distributed at the regional level (again, by the largest remainder method of PR), and then among multi-member colleges in regions with two or more colleges, in the manner previously described for the Chamber of Deputies. However, in the Senate’s case the resulting seat distribution for all colleges in a given region (rather than a multi-member district) is compared with the distribution of seats at the regional (rather than district) level.


      • My website’s Italy page now has the definitive results of last March 4 election for the Chamber of Deputies in Italy proper minus Valle d’Aosta, as issued (and subsequently corrected) by the Supreme Court of Cassation just over two weeks ago. While the vote totals had some comparatively minor changes with respect to the preliminary figures, the nationwide distribution of Chamber seats remained unchanged; in the ten single-member colleges which remained undeclared on election night, the leading candidates at the conclusion of the preliminary count ultimately won their respective seats.

        Although the initial allocation of Chamber seats among the twenty-seven multi-member districts was identical (after the aforementioned correction) to the distribution based on preliminary returns, it turned out that M5S ran out of candidates to fill all the seats assigned to the party in Campania 1 and Sicily 2, coming up short by three seats in both districts; many of the party’s list candidates were also SMC candidates, and M5S swept the election in both districts, winning every single-member college in each case. In accordance with the electoral law, the unfilled seats were then re-allocated to other districts where the party had unused fractional remainders (and then to available candidates with unused remainders at the multi-member college level), starting with the largest such remainder and continuing in descending order. Initially, it was determined the unfilled M5S mandates would be allocated to Campania 2, Piemonte 2, Calabria, Molise, Toscana and Lazio 1, but the party had run out of available candidates in Molise, so the sixth and final seat went to Puglia.

        The initial set of definitive results issued by the Supreme Court of Cassation assigned Fratelli d’Italia a seat in Calabria, at the expense of Forza Italia. However, it was determined that this was the result of a data transcription mistake by the district electoral office, which erroneously assigned about five thousand Forza Italia votes to FdI. The ensuing correction – which only affected the center-right alliance parties and had no impact whatsoever on the nationwide distribution of list seats – reverted the disputed seat back to Forza Italia, but the switch triggered a cascade effect, as FdI then had to give up a seat in Veneto 1 to the Lega, which in turn recovered a seat from Forza Italia in Trentino-Alto Adige; in turn, the Forza Italia candidate losing the seat in the latter district displaced a fellow party candidate in Emilia Romagna, as she was running in multi-member colleges in both districts and remained entitled to a seat in the latter. Meanwhile, the Italian press had a field day with the whole fiasco, writing of “chaos” in “half the country” over the allocation of Chamber list seats, and even describing the workings of the electoral system as “infernal.” I subsequently thought the latter assertion might not be that far-fetched, if one considers the absence of an overall majority has left the Italian Parliament in limbo, at least for the time being.

        But seriously, the whole mess appeared to be triggered by Rosatellum bis’ reliance on the largest remainder method, which is notoriously sensitive to small fluctuations in the party vote totals. As a purely mathematical exercise, I carried out the allocation of list seats using a variation of Norway’s electoral system, which is based on the modified Sainte-Laguë method; I used the non-modified form, which has an initial divisor of one instead of 1.4, and retained the thresholds established by the Rosatellum bis electoral law. While this system produced a slightly different distribution of seats at the district level (the nationwide allocation was identical to the actual outcome in any case), the error in Calabria had no impact whatsoever when district seats were allocated by the Sainte-Laguë method (on the downside, had no seats changed hands, the error might have probably passed unnoticed). Finally, both Rosatellum bis and the Norwegian system allocated Molise’s single list seat to the Free and Equal ticket, despite the fact that it finished a poor fourth in the district, with just 3.7% of the vote.


    • I have come across a very interesting finding which I believe might explain the oft-repeated claim that 40% of the votes would have delivered an overall parliamentary majority in Italy’s general election. Specifically, if Italy is split in two zones – one in the north comprising Northwest Italy, Northeast Italy and Central Italy (as defined by the Italian National Institute of Statistics), and the other in the south formed by the rest of the country (that is, South Italy and the islands of Sicily and Sardinia), it turns out that in the north the center-right coalition won 107 of 151 Chamber of Deputies SMC seats (70.9%) with just over 40% of the votes, and more importantly an overall majority of 216 out of 403 seats (53.6%); both M5S and the center-left coalition won 26.1% of the vote there, with the latter ahead of the former by fewer than five thousand votes.

      In other words, the claim actually turned out to be true for nearly two-thirds of Italy. But two-thirds of a country is not a country: in the south, M5S won a sweeping victory with 46.4% of the vote, capturing 76 of 80 SMC seats; the center-right coalition polled 30.7% of the vote but only won the remaining four SMC seats, while the center-left received just 16.1% of the vote and won no SMC seats. Even after the allocation of PR seats M5S still had a disproportionately high 65.4% share of Chamber seats in the area (140 of 214 seats). In fact, the slightly disproportionate outcome of Italy’s election was actually the product of two substantially disproportionate outcomes for different winners in the north and the south, which largely cancelled each other out.

      At any rate, it would seem that the 40% claim originated out of the expectation that the winning center-right coalition would also carry the south, as had been the case in previous center-right victories. In fact, in mid-January MSS re-tweeted a set of seat projections based on an opinion poll taken in Italy around that time, which had the center-right falling short of an overall majority: the SMC seat regional projections called for the center-right to win a clear majority of SMC seats, but while the figures for the north were roughly in line with the actual outcome (the scope of the center-right’s victory was somewhat underestimated, mainly because of the center-left’s seat projection over-estimate), the seat projections for the south – which had the center-right winning a clear majority of SMC seats in the area – could not have been further removed from reality.

      As it turned out, while both parts of the country rejected the center-left (which lost 5.2% in the north and 9.7% in the south), the center-right and M5S had almost diametrically opposite swings: in the north the center-right’s share of the vote soared by twelve percentage points, but M5S’ went up just 1.3%; however, in the south M5S scored a dramatic 19.3% increase, while the center right slipped back by one percent.

      Now, one question remains: would it have been possible for the center-right coalition to win an absolute majority of seats in all of Italy had it reached 40% of the vote, by having a sufficiently higher vote total in the south at the expense of M5S? As it turns out, the answer is possibly yes. Had the center-right’s share of the vote in the south been 9.25% higher (and M5S’ 9.25% lower), the coalition would have polled just over 40% of the nationwide vote; moreover, had this shift been uniformly replicated in the eighty southern SMCs, it would have caused M5S to lose fifty-one seats to the center-right coalition; interestingly enough, the resulting 55-25 SMC seat distribution would have been more in line with the January seat projections. Moreover, the 9.25% increase in the south would have allowed the center-right to win an extra twelve PR list seats. In all, the center-right would have had sixty-three additional seats – enough to secure a 328-302 majority in the Chamber of Deputies.

      Nevertheless, thirty-one SMC seats in the south would have been decided by margins of less than five percent (23 for the center-right and eight for M5S), and the popular vote outcome in the area would have been relatively close, with M5S standing at 37.1% to the center-right’s 40%; in the actual results, only five southern SMC seats were decided by majorities of less than five percent, of which M5S carried three and the center-right the remaining two. As such, these figures should be taken with a fair amount of caution, all the more so in light of the fact that the swings towards M5S varied considerably among the southern regions.


      • Thanks, Manuel. Related to this, I did see a table that someone at an Italian research institute apparently circulated to journalists that shows scenarios that were of the sort: An alliance would need around this percentage of the vote to win a majority of seats IF it won this percentage of the single-seat districts. And sure enough, it had 40% of the votes plus 70% of the SSDs likely resulting in a majority.

        This somehow got turned into “40% required” or “if they’d reached 40% they’d have had a majority” in some of the journalists’ write-ups. Which was not actually what the table said.


  5. “mixed member not-so-proportional system”

    I have to admit that I was puzzled by the use of “mixed member majoritarian” (MMM) to describe an electoral system like Itay’s. There is nothing majoritarian about it. The single member districts are won by pluralities, not majorities. And there are no bonus seats or other devices to create a majority in the legislature if the voters don’t.

    Isn’t “mixed member non-proportional” (MMNP) a better term for systems where members elected from single (or dual) member districts and members elected proportionally from multi-member districts are both in the same legislative chamber, but there is no adjustment made to ensure the overall result is proportional?


    • Ed, it is MMM by the definition of such a system, as explained in the post. I am using the definition of Shugart and Wattenberg (2001).

      The Italian system is not even a hybrid. So there is no need to invent a new term or acronym. I was joking in my response to Manuel, and I assumed he was joking as well.

      If you are objecting to the term, majoritarian, well, it is pretty firmly established as a broad concept covering FPTP and other plurality-base systems, and in contrast to the other broad category of proportional. Hence two broad types of mixed-member system: MMP and MMM, according to whether list allocation is compensatory or not.

      I also refer you to the extensive discussion of the Italian system and its type in the comments to an earlier post.


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  7. On Manuels comment #29627 (11/03/2018 at 8:46 am): such a distribution of seats (how to fill the cells if rows and column totals are predetermined) can be done much more easily by the birporportional apportionment (see wikipedia article)


    • I had read many years ago about the implementation of bi-proportional apportionment in Zurich, but as I seem to recall the described procedure was different from the one shown in the Wikipedia article. At any rate, perhaps you should pass that information on to the members of the Italian Parliament, as there is talk of changing the electoral system again (that said, I’m a bit skeptical anything is going to come out of it, at least right away).

      It would seem that every so often one comes across totally unrealistic expectations regarding the types of outcomes electoral systems can deliver. In the United States, some folks are expecting FPTP to behave in a proportional manner, while in Italy a mixed system is somehow expected to produce an overall parliamentary majority for the winner when that goal cannot be achieved even within the system’s SMC component.

      All the same, there’s one way Italy could have a working parliamentary majority, and that would be accomplished by switching to block voting, with winner-take-all multi-member districts or regions. However, in my view the remedy could be worse than the disease: while the notional distribution of legislative seats would result in clear center-right majorities in both houses of Parliament – 338 seats in the Chamber and 167 in the Senate (excluding Valle d’Aosta, Trentino-Alto Adige and the seats set aside for Italians residing abroad), the center-right would not have a single parliamentarian from the south in either chamber, and this state of affairs could easily devolve into a government of the north, for the north and by the north, especially if the implementation of block voting were to be extended to the allocation of alliance seats. Under that particular scenario, the League would end up with all of the center-right’s Chamber seats and 139 of the alliance’s 167 Senate mandates, since it was the largest constituent party in all but one of the districts or regions in which the center-right won seats (the exception being Lazio region, and only for the Senate). As such, the hard right, despite being clearly in the minority, would have practically full control by virtue of the block voting system and an alliance with a moderate right that would nonetheless find itself largely sidelined, despite being on the winning side. Sounds familiar, doesn’t it?


      • And, of course, there would be greater issues with block voting (which I take here to mean Singapore-style largest-party-wins-everything) in a close election, where one coalition could end up with a majority in one house and another coalition could end up with a majority in the other (owing to differential voting ages). It also wouldn’t get rid of the issue of small parties having ‘blackmail’ power over larger ones by insisting on disproportionately large shares of seats on coalition lists (as I think ‘Noi con l’Italia’ did this time), so coalitions, even with a majority, might still have trouble governing (as Romano Prodi did after the 2006 election).


      • Or majority reversals for that matter, which is exactly what would have happened in 2013: Silvio Berlusconi would have won absolute majorities in both the Chamber and the Senate, despite arriving second and polling less than one-third of the vote in both cases. Moreover, the Chamber result would have been decided by very narrow majorities for Berlusconi in Lombardia 1 and Friuli-Venezia Giulia, the latter a close three-way race between Berlusconi, Bersani and M5S. And speaking of Beppe Grillo’s outfit, it would not have done too badly in the Chamber, but it would have been shut out of the Senate in Italy proper because in the upper house vote the party didn’t top the poll in any region back then.

        Incidentally, the notional center-right Chamber majority in 2018 under block voting would have hinged on the election outcome in the Lazio 1 multi-member district, which covers almost the entire Rome metro area and where the center-right coalition held a paper-thin lead over M5S, with some polling stations yet to be tallied.


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