Competition among parties and power: An empirical analysis

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1 ISSN: POLIS Working Papers [Online] Dipartimento di Politiche Pubbliche e Scelte Collettive POLIS Department of Public Policy and Public Choice POLIS POLIS Working Papers n. 197 February 2012 Competition among parties and power: An empirical analysis Matteo Migheli, Guido Ortona and Ferruccio Ponzano UNIVERSITA DEL PIEMONTE ORIENTALE Amedeo Avogadro ALESSANDRIA Periodico mensile on-line "POLIS Working Papers" - Iscrizione n.591 del 12/05/ Tribunale di Alessandria

2 Competition among parties and power: An empirical analysis Matteo Migheli* Guido Ortona* Ferruccio Ponzano* Abstract According to commonsense wisdom, under proportionality a small centrist party enjoys an excess of power with reference to its share of seats (or votes) due to the possibility of blackmailing the larger ones. This hypothesis has been challenged on a theoretical ground, with some empirical support. In this paper we use simulation to test its validity. Our results strongly provide evidence that the hypothesis is actually wrong. What occurs is a transfer of power from the peryphery of the political spectrum towards the center, buth the major gainers are the large centrist parties and not the small ones. * University of Eastern Piedmont, Department of Law, Economics and Political Sciences, Via Cavour, Alessandria (AL) Italy. Corresponding author: tel.: matteo.migheli@sp.unipmn.it 1

3 1. Introduction. In this paper we test through smulation the hypothesis that under proportionality small centrist parties enjoy an (undeserved) excess of power. This is quite a common wisdom. For instance, an authoritative source addressed to policymakers (IDEA, 2005, p.57), claims that "[under proportional representation] tiny minority parties [can] hold larger parties to ransom in coalition negotiations. [...] Small parties get a disproportionately large amount of power. Large parties may be forced to form coalitions with much smaller parties, giving a party that has the support of only a small percentage of the votes the power to veto any proposal that comes from the larger parties". What above looks highly plausible, yet it may be contrasted on a theoretical ground, and actually has been. Non-constrained proportionality propitiates the birth of small "blackmailing" parties, but at the same time creates competition among them. This competition may lead to the dissipation of the whole rent accruing to the small parties; this occurs when they are so many that the power of each is just what suffices to justify its existence, and this threshold may well correspond to an endowment of power not significantly greater than the share of seats. This is what has been argued convincingly in a recent paper (McGann et al., 2009), where empirical and simulative evidence is also provided. Previously, at least two results pointing into the same direction were obtained. Gelman et al. (2004, p. 658) found that "All the standard measures of theoretical voting power yield the counterintuitive result that, in a proportional voting system, voters in large districts tend to have disproportionate power. [...] The most important political implication of our findings is that proportional weighting systems are, in fact, basically fair to all voters"; and Snyder et al. (2005) "find that each voter s expected payoff is proportional to her voting weight" (2005, p.981). Actually, the examples that seemingly support the claim that small parties enjoy too much power, like Bomsdorf (1982), who does find an excess of power for a minor party in the German Bundestagand, and Johnston (1982), who finds an excess of power for small countries in the (then) nine-member European Parliament, usually fail to take into account the contendibility of the political market. In Germany a 5% threshold prohibits the entry of too many small parties, and of course there was no free entry in the European Parliament. In the spirit of Downs, an analogy with the fate of extra-profits in a competitive economy is not out of place. Extra-profits are driven towards zero by the entering of new firms; analogously, new parties are attracted by the political extra-profit stemming from an excess of power, and they will keep on entering until the extra-power is fully dissipated. Not by chance, in the country that has come to epitomize the typical features of proportional representation, i.e. Italy, government coalitions were typically not minimum winning coalitions of parties. As suggested above, our approach is inductive. We will provide examples obtained through simulation on realistic stylized cases. The procedure assumes the same set of preferences of the 2

4 voters across the electoral systems, hence all differences will be produced by the electoral system. The indices of power commonly employed assume that all the coalitions are possible. The assumption is clearly unrealistic, but is often unavoidable if one wants to produce general results. However, when analyzing specific cases the plausibility of the coalitions must be taken into account. We will do that through the use of a duly modified Banzhaf index, to be presented and discussed in section 2. It is useful to anticipate that our results strongly support the hypothesis that small centrist parties typically do not enjoy excess power, with some interesting qualifications. 2. Methodology. We will compare the parliaments and the government majorities resulting from the same set of preferences of the voters under three proportional systems: pure proportionality, threshold proportionality and single transferable vote. To compare the Parliaments produced by different electoral systems given the same set of preferences we employed the simulation program ALEX4.2, developed at the Università del Piemonte Orientale by one of the authors and other collaborators 1. As stated above, we adopt an empirical approach. It is obvious that to try to infer from a real plurality or run-off case the number and dimensions of would-be parties in a proportional system, given the same set of preferences of the voters, is highly hazardous. On the contrary the opposite is much more plausible. This forces us to use as case studies only countries that actually adopt a proportional system, possibly a highly proportional one. We will consider three countries, i.e. Germany, Italy and The Netherlands; actually a sketch of them, due to the limits of the simulation program, but as we will see these limits are fairly broad 2. Hence, the input is made basically of the votes that each party received in the last election of the Lower Chamber for The Netherlands and for Germany, and in the last as well as in the second to last for Italy 3. In addition, we built also an artificial case displaying some main features that are considered typical of a proportional system and that are relevant for our discussion, i.e. relatively strong extreme parties and several small centrist parties. As anticipated, the power indices currently available are not suitable for our purpose. In the last couple of decades there has been an enormous debate on the merits and pitfalls of a number of power indices (see f.i. Felsenthal and Machover, 1998 and 2001; Journal of Theoretical Politics, 1999). No need to enter into this debate; it is sufficient to state that for our purpose all the indices 1 For a broader description (actually, of a previous version) see Bissey and Ortona (2007). Some features employed here are detailed only in the readme file accompanying the program, downloadable from the site 2 With reference to the real cases, the main changes are that we did not consider the geographical clustering of votes, and that we assumed a unique, nation-wide district (which is true only for The Netherlands). 3 The number of parties that obtained seats in the Parliament was very different in the two Italian polls, hence both cases are of interest. 3

5 have two flaws. First, they assume either that all possible coalitions are equally likely (a coalition between Christian Democrats and Social Democrats is weighted no differently from a coalition between Fascists and Communists), or they require the specification of a graph structure highly arbitrary and cumbersome. The first case is that, for instance, of Banzhaf or Shapley-Shubik, the second that of Owen. Second, they usually assume that the share of seats of a party is not relevant per se, as only the coalitional pivotality matters. In the classical textbook case of three parties with 49, 2 and 49 seats the Banzhaf index assigns the same share of power to each one. Clearly, in the reality this is not true, be it only for the relevance of the local power of the MPs, and as may be easily seen looking at the distribution of the ministries in coalition governments 4. Some attempts have recently be made to define more realistic indices (see among others Aleskerov, 2006; Chessa and Fragnelli, 2011; Fragnelli, Ottone and Sattanino, 2009; Alonso- Meijide et al., 2009; Mielcová, 2010; Migheli and Ortona, 2011). This approach is still in its beginning; drawing on it, we defined a new empirical index, that we labeled 5. It is a modified Banzhaf index, computed as follows. a) ALEX4.2 individuates all the contiguous majority coalitions 6. b) For every contiguous majority coalition it assigns to each party a score made of two components. In the first, bb i, B i takes value 1 if the party is pivotal 7 and 0 if it is not, while b is a weight that ranges between 0 and 1; the second is equal to the share of seats of the party in the coalition, weighted with the factor (1-b). Basically b serves to weigh the two components of the power of a party: that measured by the Banzhaf s index and that given by the share of seats in the chamber. The value of b must be established by the programmer; this way s/he may decide what is the relative relevance to be assigned to the share of seats and to being or not pivotal. c) For each party, the scores obtained in all the contiguous majority coalitions are summed up, thus providing a non-normalized index, n = bb + ( 1 b) i j ij d) Finally, the index is normalized [0-1] by dividing it by the sum of the non-normalizes indices. In symbols, i = ni n i i S S ij j 4 Snyder et al. (2005, p.993) find that the share of seats affects positively and strongly the power of a governing party. 5 For ALEX power index. 6 A contiguous coalition is a coalition of parties adjacent on the (assumed) left-right axis. In other terms, no "holes" are allowed in a majority coalition. 7 A party is pivotal (or crucial) when a coalition to which it belongs loses the majority if that party leaves it. 4

6 where i refers to parties, j refers to contiguous majority coalitions, B ij is the Banzhaf power score of party i in the contiguous majority coalition j, S ij are the seats of party i in the contiguous majority coalition j and S j are the total seats of the majority coalition j. Note that if b=1 i collapses to a modified Banzhaf index computed only across contiguous coalition, while if b=0 all what matters is the share of seats in the majority coalitions 8. The meaning of may be summarized as follows. First, we assume that all the variables that determine the power of a party are strongly correlated either with its cruciality or with its share of seats. Second, the requisite of contiguous coalitions excludes implausible ones ("fascists + communists") Results. In our simulations the distribution of power resulted quite insensitive to the value of parameter b, unless its value was 1, hence we will consider only the value 0.75, for sake of simplicity and to avoid a flood of data may be considered a conservative figure with reference to the hypothesis to be tested in this paper, because the power of small centrist parties is arguably related positively to the value of b, i.e. to the weight of the cruciality with respect to that of the share of seats A realistic exemplum fictum. We suppose a fictitious State whose (one-chamber) Parliament is made of 200 Members, to be elected in districts of the same magnitude. There are 20,000 virtual voters, a figure much larger than usual pre-electoral polls in a typical European country. No one will abstain. At the start, there are 5 parties, ordered left to right and labelled A to E; they enjoy respectively 14, 32, 10, 28 and 16% of votes (or of first preferences). Arguably, this case is sufficiently typical, with two main centrist parties, a relatively small centrist party and two more extreme ones. Our small centrist party (not that small, for the moment) is obviously C. Then it splits into two, C1 and C2, with 5% of votes each, and finally into three, C1 with 4.1%, C2 with 2% and C3 with 3.9%. We introduced a couple of asymmentries, to avoid unconvenient (and unrealistic) perfectly symmetric results 11. Let's start with pure proportionality (table 1). 8 Mazurkiewicz and Mercik (2005) also suggested an index that takes into account the preference of the parties for the coalitions, based on a modified Shapley-Shubik index. 9 The possibility of the "bypassing" of a party may be excluded on the basis of simple theoretical considerations. Assume that all parties prefer being in the government to being outside it. Now suppose that two parties, A (a large one) and C (a minor one) have enough seats to form the Government. On the left to right axis party B lies between them. A will prefer to summon it in the government, to reduce the power of C; C may opposite menacing to withdraw, but the menace is not credible. 10 For instance, the values corresponding to the third column of table 1 with b=0 resulted for A, for B, for C, for D and for E. Analogous results obtained for the other simulations. 11 These figures may differ slightly from the share of seats and across simulations also in pure proportionality, due to the random component of the simulation program - see the readme of the program ALEX 4.2, referred to in fn. 2. 5

7 Table 1. Pure proportional system (D'Hondt). Values of, b=0.75. DM is short for district magnitude. One small centrist party. Party share DM 200 DM 20 DM 10 of seats A B C D E Assuming as a benchmark the share of seats, some 6% of the total power is shifted to party C. But what is relevant is not whether a small centrist party gains power, but wether it gains power with respect to the large centrist parties. This is actually what happens. Party C will enter in a coalition either with party B, who gains some 1% of power, of with party D, who gains a little less than 2% (or with both). However, party C is not that small; actual small centrist parties are usually much smaller. Let'see what happens in a more realistic case, where party C divides in two smaller parties, C1 and C2, each with 5% of the seats (table 2). Table 2. Pure proportional system (D'Hondt). Values of, b=0.75. DM is short for district magnitude. two small centrist parties. Party share of seats DM 200 DM 20 DM 10 A B C C D E The situation changes quite dramatically. The gain of power of the two C parties is of 3.80% and 1.41% respectively with a DM of 200, to be compared with a gain of 5.48% of party B and a loss of 2.54% of party D. Together, the two small parties gain less power that the main large party. The DM acquires relevance: with a DM of 20 the overall gain of small centrist parties is 2.90%, while B obtains 6.85% (not to speak of the DM of 10, where the small parties disappear). 6

8 However, both in Italy (13 polls since 1948) and in the Netherlands (11 polls with 150 MPs since 1977) there has been only one case with less than three small centrist parties 12. Hence it is of interest to see what happens with three small centrist parties (table 3) 13. Table 3. Pure proportional system (D'Hondt). Values of, b=0.75. DM is short for district magnitude. three small centrist parties. Party share of seats DM 200 DM 20 DM 10 A B C C C D E In this case the gain of C-parties is much smaller than that of a large party. Even in the most favourable case (column 3), the overall gain of the three is 4.16%, against 8.91% of party B. The (seemingly alleged, in our case) excess power of small parties may be contrasted in two ways, either through the reduction of the district magnitude of through the introduction of a threshold. As may be seen in the previous tables, tha first system is actually effective in our simulation, but the price to be paid is high, i.e. the assignment of a considerable excess power to a large party: as much as nearly 20% in column 4 of the case of table 3, that we saw to be the most realistic one. Let's now see in table 4 the result of the adoption of a 4% threshold. With one or two small centrist parties the threshold is ineffective, and with a DM of 10 none of them gets a seat. Table 4. Threshold proportional system (4%; D'Hondt). Values of, b=0.75. DM is short for district magnitude. three small centrist parties. Party share of seats DM 200 DM 20 DM 10 A B C C C D E The case of Germany is different, given the adoption of the 5% threshold. However, in the only post-war poll without the threshold (1949) there were ate least 4 small centrist parties (the number varies according to the assumed location of the parties on the left-right axis). 13 We tried several distribution of seats among the three, without relevant changes; the following one may be considered representative. 7

9 As expected, the effect is similar to that of a reduction of district magnitude. With a DM of 200 the overall gain of power of small centrist parties decreases with respect to pure proportionality, and with a DM of 20 they lose power. Clearly, this result is due to the implicit threshold that inhibits small parties from obtaining seats in some to most (or all) constituencies. However, the price to be paid is very high: nearly 8% of excess power to the largest large party in the first case, as much as more than 21% in the second. A further exercise concerns the single transferable vote. Due to its very nature, this system does not perform well with large districts, hence we supposed 20 districts each with a DM of 10. The results are in table 5 to 7 for the three cases of one, two and three small centist parties. The distribution of the first preference is the same as that of votes in the previous analysis. Table 5. STV (Hare). Values of, b=0.75. District magnitude = 10. One small centrist party. Party share of seats A B C D E Table 6. STV (Hare). Values of, b=0.75. District magnitude = 10. Two small centrist parties. Party share of seats A B C C D E Table 7. STV (Hare). Values of, b=0.75. District magnitude = 10. Three small centrist parties Party share of seats A B C C C D E

10 The results are broadly in line with those of the other two systems in what concerns the order of magnitude of the redistribution of power; they are quite different in what concerns the hierarchy of the gains. If there is only one small centrist party, it enjoys a considerable gain in share of power with respect to the share of seats; actually, more than under pure proportionality. If the parties are two or three, they gain much less, but still more than the larger parties, differently from the previous cases. We may summarize as follows the results of the simulation of our fictitious Parliament: a) The redistribution of power with respect to the share of seats occurs from the periphery of the political space towards its center, much more than within the center; b) The (alleged, up to now) gain of power of the small centrist parties is in any case not that large; even in the most favourable instance (STV, one party) it is made of an one-digit figure; c) The real gainers in share of power are not the small parties, but the large ones (or one of them); d) At first sight, a reduction of proportionality, either through district magnitude or through a threshold, does reduces the gain of power of small parties, even if the reduction is smaller than the additional gain of the large ones. e) However, the previous result produces only if small parties keep on participatinng in the polls despite the threshold, be it formal or implicit in the district magnitude. It is more realistic to suppose that a threshold will reduce the number of parties running for seats. This case is depicted in table 1: and as we see the not-so-small party produced by the merging of would-be small ones gains a lot of power. This suggests that a policy aiming to reduce the (supposed) power of small centrist parties through the adoption of a threshold may well be counterproductive. Also, this confirms the theoretical insight quoted in section 1: small centrist parties dissipate the power rent, unless the competitive entry is obstructed. f) STV is not a remedy to the excess power of small parties; instead, it looks a good preventer of an excess power of the large ones. Now let's move to the real world cases The Netherlands. The data for the Netherlands appear in table 8, and they are in line with those of the previous sub-section. To some degree, the ordering left-to-right is a matter of opinion; we assumed that only two parties may be considered small centrist parties, i.e. the not-that-small SP and the much smaller CU. 14 For the real world cases we excluded some minor parties (with less than 1% of votes and no seats); as a consequences our data may be slightly different from the official ones. 9

11 Table 8. The Netherlands (2010 election)., b= Party Pure prop., Share of seats Pure prop., 5% thresh. share of seats 5% threshold, 5% thresh. share of seats, with CU and SP united 5% thresh. with CU and SP united STV, share of seats STV, D GL PvdD PvdA SP CU CDA SGP VVD PVV Under pure proportionality, the two small parties together gain some 3% of power with respect to the share of seats, to be compared with the 2.1% obtained by PvdA and with the 6.41% of CDA. A 5% threshold would be effective: CU would disappear and SP would lose power. In this case too, however, the two larger parties would enjoy a considerable transfer of power, nearly 10% altogether. For proportionality the general results of the fictitious example are confirmed: there is a transfer of power from periphery to center; the gain of power of the small centrist parties is minor; that of the large centrist parties is greater; if small parties do not merge a threshold is effective in reducing the power of small centrist parties, but greatly increases that of the larger ones; if small parties merge a threshold is counterproductive. Finally, the effect of STV is very similar to the fictitious case with reference to small parties (a moderate gain of power) and more erratic with reference to the large ones, where one of them gains more than 6% of power, and the other less than 3% Italy. In tables 9 and 10 we show the results of the two last elections in Italy, 2006 and We simulated both because of the large differences between their results. The Italian systems is characterized by the presence of two main parties, Ulivo and FI in 2006 and PD and PDL in 2008 (actually the same as before, under different names). They are located in the centre-left and in the centre-right. There are also several small parties in the left, in the centre and in the right. 15 For proportional systems 1 district with a magnitude of 150 and 15,000 voters; for STV 15 districts with magnitude 10 and 1000 voters each. 10

12 Table 9 Italy (2006 election)., b=0.75 Party Pure prop., Share of Seats Pure prop., 5% thresh. share of seats 5% threshold, 5% thresh. share of seats, with small centrist parties united 16 5% thresh. with small centrist parties united STV, share of seats STV, PRC PCI Verdi Ulivo SVP RnP IDV UDEUR UDC DC-PSI FI LN AN In 2006 and in proportionality, we find again that extreme parties transfer power to the centrist ones, both large and small. The gain of the large ones is limited, but greater than that of the small ones; as expected, the competition among the small parties dissipates their power rent. There is however one exception, that of UDC, which is the greater gainer. The most plausible interpretation is that the plethora of small parties leaves to UDC a lot of cruciality. Contrary to what may appears at first sight, this result supports the hypothesis of McGann et al. that small centrist parties do not enjoy excess power. They obtain them only if they remain sufficiently large, but the rent is dissipated if they are too many and hence too small: and UDC is not that small. There is a good reason for that: UDC is a Catholic party, strongly supported by the Church, aiming to be the heir of the historic Christian Democratic Party. Hence a possible tendency towards its fragmentation was, and is, contrasted by a substantial tendency towards its unity. With a 5% threshold the only surviving small centrist party, UDC, gets some extra-power, but much less than the larger centerright party, PDL. Finally, a most evident result is the conspicuous gain of power by the small centrist parties under STV. Again, if the small centrist parties unite the threshold is ineffective, actually counterproductive if the aim of the threshold is to limit their alleged excess of power. The power of the United Parties 16 The union of centrist parties group SVP, RnP, IDV, UDEUR, UDC, DC-PSI, the results appear in the row of the first. 11

13 rises to 22.07%, as against a total of 20.3% under pure proportionality. The transfer of power under STV also favours the small centrist parties, but the pattern is more erratic 17. Table 10 Italy (2008 election)., b=0.75 Party Pure prop., Share of Seats Pure prop., 5% thresh. share of seats 5% threshold, 5% thresh. share of seats, with small centrist parties united 18 5% thresh. with small centrist parties united STV, share of seats STV, SA PD IDV PS UDC PDL LN MPA DFT In the 2008 election Italians voted largely for the right, with an enormous loss of power of the greater party of the left, the PD. Also, the number of parties in the Parliament collapsed. Only three small centrist parties survided, and among them only UDC gained some power with respect to to the share of seats, but very little, and much less than PDL, both in pure and in threshold proportionality. Again, under pure proprtionality the small parties again enjoy a very limited excess of power, just a small fraction of what is obtained by the largest party, thus confirming the theory of Gelma et al. Also, again the threshold would have been ineffective in reducing the power of the small centrist parties: if the small party do not unite they reduce to one, which enjoys an overall excess of power; and if they do they suffer a very small loss, but the increase of the share of seats makes their power greater than under pure proportionality. Finally, under STV the largest of the small centrist parties would have obtained quite an increase of power, albeit in this case less than the major party of the right Germany. Table 11 presents the results of our simulations for Germany, based on the 2008 federal election. The focus of the paper is on the power of small centrist parties, and Germany does not feature such parties, due to the 5% threshold. Nevertheless we include this country as it confirms a relevant result: even without small centrist parties that may in a way obscure the picture, 17 It must be emphasized that the hypothesis of contiguity of the coalitions may disturb the data, given the high number of small parties and their small dimensions. 18 The Union of Centrist Parties group IDV, PS, UDC 12

14 there is clearly a large displacement of power from the periphery towards the center. Under the pure proportional system, both the SPD and the CDU-CSU gain power with respect to their shares of seats: in particular the SPD gains almost 5 percentage points, while the CDU-CSU almost 10. As for the small parties, once more we notice that as they get farther from the center they lose power (with respect to their number of seats). So, for example, while the Grüne loses 4.26 percentage points over 9.03 (their share of seats), the Linke loses as much as 9.28 points over Table 11 Germany (2008 federal election)., b=0.75 Party Pure prop., Share of Seats Pure prop., 5% thresh. share of seats 5% threshold, STV, share of seats STV, Linke Grüne Ecologists SPD CDU-CSU FDP NPD Analogous results obtain under a 5%-threshold proportional system. However it is noteworthy that the largest party (CDU-CSU) gains here more than the second largest (SPD) with respect to the previous electoral system. The same center-periphery dinamics as before holds also here. The simulation for the STV highlights two major results. The first is that, not surprisingly, some small parties increase their shares of seats considerably with respect to the pure proportional case. The second is that, also under this system, analogous changes as before in the shares of power with respect to those of seats are found. It is relevant that while the largest party loses several seats in the STV with respect to to the pure proportional system, its share of power remains above the share of seats it has in the pure proportional system. The only extreme party which gets seats (the Linke) suffers a very large disproportionality between real power and share of seats. Taken together all these results confirm that the power tends to concentrate in the large centrist parties, which eat some of the power of the other parties. Conclusions Our results are inductive, hence we cannot draw conclusions, but only suggestions. However these are quite clear; they may be summarized as follows. 1. The simulations performed for this article show that the small parties do not get disproportionate power in proportional systems; hence they provide support for the theory proposed by Gelman et al. 13

15 2. A threshold may well be counterproductive as a tool to reduce the power rent of the small centrist parties: if they unite, they typically increase their power with respect to the share of seats As for the STV, the results are not that clear. All we can suggest for the moment is to pursue further the simulative research. 4. Two interesting ancillary results are that the extreme parties lose much power with respect to their shares of seats and that the large majority parties actually enjoy more power than their shares of seats. The first result is due mostly to the (realistic) assumption of contiguous coalitions. The second result show that the large parties are those who eat the power lost by the extreme parties. The implications for the positive analysis are quite clear; the normative ones much less. A fairer distribution of power could correspond to less governability, and this rules out the possibility of assuming straightforwardly a fair distribution of power as a goal, even if, in the words of Nurmi (1982, p.206), "It is evident that the idea of representative democracy rests on this identity [between the distribution of support and the distribution of voting power]". In other terms, it may still be desirable to reduce the power of the small parties and to increase that of large ones, possibly to the point of moving to a non-proportional system. But it should be clear that such a choice has to be paid with a loss in representative democracy. Our results suggest that a major argument against proportionality, that is that it actually is not really proportional because it assigns a blackmailing power to small parties, does not hold. Also, the adoption of a threshold may turn not to be a good idea: it may produce a loss of the proportionality while at the same time increasing the power of small centrist parties. 19 The reduction of the number of parties, albeit ineffective in reducing the power rent, could be desirable as it reduces the transaction costs among the parties. This topic has been considered by Migheli and Ortona (2011); we will not discuss it here as it is out of the scope of this paper. 14

16 References Aleskerov, F. (2006), Power Indices Taking into Account Agents' Preferences, in B. Simeone and F. Pukelsheim (eds.), Mathematics and Democracy, Springer, Berlin-Heidelberg, Alonso-Meijide, J. M., M. Alvares-Mozos and M. G. Fiestras-Janeiro (2009), The Banzhaf value when Some players are Incompatible, "Homo Oeconomicus", 26, 3/4, Bissey, M.-E. and G. Ortona (2007), The program for the simulation of electoral systems ALEX4.1: what it does and how to use it, Università del Piemonte Orientale, Working paper POLIS n. 91, Bomsdorf, E. (1982), The Distribution of Power in Specific Decision-Making Bodies, in Holler (ed., 1982). Chessa, M. and V.Fragnelli (2011), Embedding classical indices in the FP family, "AUCO Czech Economic Review", 5, Gelman, A., J. N. Katz and J. Bafumi (2004), Standard Voting Power Indexes Do Not Work: An Empirical Analysis, "British Journal of Political Science", 34, Felsenthal, D. and M. Machover (1998), The measurement of voting power, Elgar, Cheltenham. Felsenthal, D. and M. Machover (2001) Myths and Meanings of Voting Power: Comments on a Symposium, "Journal of Theoretical Politics", 13, Fragnelli, V., S. Ottone and R. Sattanino (2009), A New Family of Power Indices for Voting Games, "Homo Oeconomicus", 26, 3/4, International Institute for Democracy and Electoral Assistance (IDEA, 2005), Electoral System Design: The New International Idea Handbook, IDEA, Stockholm. Johnston, R. J. (2000), Power Indices and the Design of Electoral/Constitutional Systems, "Homo Oeconomicus", 17,

17 Journal of Theoretical Politics (1999): Symposium on the Power Indices, 11, 3, Mazurkiewicz, M. and J. W. Mercik (2005), Modified Shapley Shubik power index for parliamentary coalitions, "Operations Research and Decision", 2, McGann, A., J. Ensch and T. Moran (2009), The Surprisingly Majoritarian Nature of Proportional Democracy, Paper presented to the Annual Meeting of the American Political Science Association, Toronto, September 3-6, Mielcová, E. (2010), The Uncertainty invoting Power: The Case of the Czech Parliament , "AUCO Czech Economic Review" 4, Migheli, M. and G.Ortona (2011), Plurality, Proportionality, Governability and Factions, "Representation", 47, 1, Nurmi, H. (1982), The Problem of the Right Distribution of Voting Power, in M. J. Holler (ed.), Power, Voting and Voting Power, Physica-Verlag, Wűrzburg and Wien, Snyder, J. M., M. M. Ting and S. Ansolabehere (2005), Legislative Bargaining under Weighted Voting, "American Economic Review", 95, 4,

18 Recent working papers The complete list of working papers is can be found at *Economics Series **Political Theory Series T Territories Series Q Quaderni CIVIS ε Al.Ex Series 2012 n.197 ε Matteo Migheli, Guido Ortona and Ferruccio Ponzano: Competition among parties and power: An empirical analysis 2012 n.196* Roberto Bombana and Carla Marchese: Designing Fees for Music Copyright Holders in Radio Services 2012 n.195* Roberto Ippoliti and Greta Falavigna: Pharmaceutical clinical research and regulation: an impact evaluation of public policy 2011 n.194* Elisa Rebessi: Diffusione dei luoghi di culto islamici e gestione delle conflittualità. La moschea di via Urbino a Torino come studio di caso 2011 n.193* Laura Priore: Il consumo di carne halal nei paesi europei: caratteristiche e trasformazioni in atto 2011 n.192** Maurilio Guasco: L'emergere di una coscienza civile e sociale negli anni dell'unita' d'italia 2011 n.191* Melania Verde and Magalì Fia: Le risorse finanziarie e cognitive del sistema universitario italiano. Uno sguardo d'insieme 2011 n.190 ε Gianna Lotito, Matteo Migheli and Guido Ortona: Is cooperation instinctive? Evidence from the response times in a Public Goods Game 2011 n.189** Joerg Luther: Fundamental rights in Italy: Revised contributions 2009 for Fundamental rights in Europe and Northern America (DFG-Research A. Weber, Univers. Osnabrueck) 2011 n.188 ε Gianna Lotito, Matteo Migheli and Guido Ortona: An experimental inquiry into the nature of relational goods 2011 n.187* Greta Falavigna and Roberto Ippoliti: Data Envelopment Analysis e sistemi sanitari regionali italiani 2011 n.186* Angela Fraschini: Saracco e i problemi finanziari del Regno d'italia 2011 n.185* Davide La Torre, Simone Marsiglio, Fabio Privileggi: Fractals and selfsimilarity in economics: the case of a stochastic two-sector growth model 2011 n.184* Kristine Forslund, Lycia Lima and Ugo Panizza: The determinants of the composition of public debt in developing and emerging market countries

19 2011 n.183* Franco Amisano, Alberto Cassone and Carla Marchese: Trasporto pubblico locale e aree a domanda di mobilità debole in Provincia di Alessandria 2011 n.182* Piergiuseppe Fortunato and Ugo Panizza: Democracy, education and the quality of government 2011 n.181* Franco Amisano and Alberto Cassone: Economic sustainability of an alternative form of incentives to pharmaceutical innovation. The proposal of Thomas W. Pogge 2011 n.180* Cristina Elisa Orso: Microcredit and poverty. An overview of the principal statistical methods used to measure the program net impacts 2011 n.179** Noemi Podestà e Alberto Chiari: La qualità dei processi deliberativi 2011 n.178** Stefano Procacci: Dalla Peace Resarch alla Scuola di Copenhagen. Sviluppi e trasformazioni di un programma di ricerca 2010 n.177* Fabio Privileggi: Transition dynamics in endogenous recombinant growth models by means of projection methods 2010 n.176** Fabio Longo and Jőrg Luther: Costituzioni di microstati europei: I casi di Cipro, Liechtenstein e Città del Vaticano 2010 n.175* Mikko Välimäki: Introducing Class Actions in Finland: an Example of Lawmaking without Economic Analysis 2010 n.174* Matteo Migheli: Do the Vietnamese support Doi Moi? 2010 n.173* Guido Ortona: Punishment and cooperation: the old theory 2010 n.172* Giovanni B. Ramello: Property rights and externalities: The uneasy case of knowledge 2010 n.171* Nadia Fiorino and Emma Galli: An analysis of the determinants of corruption: Evidence from the Italian regions 2010 n.170* Jacopo Costa and Roberto Ricciuti: State capacity, manufacturing and civil conflict 2010 n.169* Giovanni B. Ramello: Copyright & endogenous market structure: A glimpse from the journal-publishing market

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