Marie-Edith Bissey, Mauro Carini and Guido Ortona (2004)
ALEX3: a Simulation Program to Compare Electoral Systems
Journal of Artificial Societies and Social Simulation
vol. 7, no. 3
To cite articles published in the Journal of Artificial Societies and Social Simulation, reference the above information and include paragraph numbers if necessary
Received: 05-Nov-2003 Accepted: 11-May-2004 Published: 30-Jun-2004
where j refers to the electoral system, n is the number of parties, Sj,i is the number of seats obtained by party i under system j, Spp,i is the number of seats obtained by party i under perfect proportionality rule (PPR), and Su,i is the number of seats obtained by party i if all the seats go to the largest party in system j .
|gf / [1/m - 1/(m+1)] = (f-t/2)/(t-t/2)|
|gf = [1/m - 1/(m+1)] (f-t/2)/(t/2)|
where t is the total number of seats in the Parliament.
|g = gm +gf = 1/(m+1) + [1/m - 1/(m+1)] (f-t/2)/(t/2)|
where m is the number of crucial parties supporting the Government, f is the number of seats of the majority and t is the total number of seats. The value of g reaches its maximum, 1, when a party has all the seats, and decreases with the increase of m, thus justifying the claim that the range of g is the interval (0,1].
|Ux > Uy iff Agarb > AGaRb||(1)|
where we write for simplicity the values of g and r for X in lower-case and those for Y in upper-case.
|Ux > Uy iff (g/G)bp > (R/r)b|
Hence the condition may be written as
|pLn(g/G) > ln(R/r)||(2)|
|p > ln(R/r)/Ln(g/G) if g > G or p < ln(R/r) / ln(g/G)||(3)|
provided that g, or G, or both are < 1.
|Table 1: r and g for eleven electoral system in an Italy-like case|
|Mixed-Member 1 °||0.337||0.755||0.254|
|Mixed-Member 2 °||0.339||0.762||0.258|
|Single Transferable Vote*||0.661||0.362||0.239|
|°||25% of seats elected through one-district proportionality|
|*||Hare quota (simple rounding was used for one-district proportionality)|
|+||4% threshold (as for real)|
|Table 2: r and g for eleven electoral system in an UK-like case|
|Single Transferable Vote||0.840||0.346||0.291|
|Table 3: r and g in another Italy-like case|
|Single Transferable Vote||0.841||0.254||0.214|
|Table 4: r and g in another UK-like case|
|Single Transferable Vote||0.886||0.379||0.336|
where X is the number of seats of the m largest (i.e. major) parties in the Government, and T is the total number of seats in the Parliament. This way, the Government keeps a majority of y if the small parties of the governing coalition defeat. In ALEX3 the value of y is fixed to 1, while m may be established by the experimenter through the assignment of the share of seats in the proportional system necessary to be considered major.
2 Approval voting has been excluded as previous experiments showed that it is inferior to Condorcet voting with reference both to G and R. See Ortona (1998).
3 For a review, see Lijphart (1994, p.67).
4 See Shugart and Wattenberg (2000), p.30; Shugart (2001).
5 For a more detailed discussion of the indices, see Ortona (2002a).
6The value of Su,i is the total number of seats for the largest party, and 0 for all the others. If several parties are the largest ones ex aequo, we take one at random.
7 ALEX3 is the third version of the program. The first one required a specific database and did not include plurinominal systems. The second is like this one, but without plurinominal systems.
8 An interesting discussion of power topics in is Mudambi et al. (2001).
9 In a previous paper, the Gini coefficient relative to the Banzhaf’s power indices was employed as an additional measure of governability; but the computing was performed outside the program. See Ortona (2002a).
10 A more detailed description of the procedure may be found in Fragnelli, Monella and Ortona (2002).
11 Here is the proof.
From U = Agarb and a =pb we get dU = dg(bpAgbp-1rb) + dr(bAgbprb-1)
If U does not change 0 = dg(bpAgbp-1rb) + dr(bAgbprb-1)
dg(bpAgbp-1rb) = - dr(bAgbprb-1)
dr/r = - p(dg/g)
12 Remember that g ≤ 1. If (trivially) the value of both g and G is 1, the value of r will establish the best system.
13 Lower Chamber only.
14 It may be of some interest to recall that in Italy some 1,500 respondents are commonly assumed to be sufficient to provide a reliable nation-wide survey.
15 See Appendix 1 for details.
16 Assuming p = 1, i.e. a = b, the selection criterion becomes "system X is preferred to system Y iff gxarxa > gyarya, i.e. gxrx > gyry. The rank of r times g provides the rank of the electoral systems.
17 See Appendix 1 for details.
18 See again Appendix 1.
19 When parties obtained (rearranged) 3.30, 45.31, 17.16, 28.78, 1.07, 3.30 and 1.07% of votes respectively.
20 Not necessarily complete.
21 Java Runtime 1.4 can be downloaded from http://java.sun.com.
22 To avoid the mushrooming of possible Governments, it is almost inevitable to adopt some rules concerning the coalition that will actually be chosen. A reasonable set is to suppose that (a) the Government must be supported by the majority of MPs and (b) the Government is made by a minimum winning coalition of parties adjacent on the left-right axis. The program could easily implement the conditions, thus producing automatically the government; however, we preferred to leave this task to the user, as condition (b) is not that frequent in real world, and it may be of interest to explore different possibilities.
23 This claim could be tested through ALEX3.
FRAGNELLI V, Monella G and Ortona G (2002) "Governability and Representativeness: Simulation of Concrete Voting Situations", paper presented to the Spanish Meeting on Game Theory and applications, Sevilla, July.
LIJPHART A (1994) Electoral Systems and Party Systems: a Study of Twenty-seven Democracies, 1945-1990. Oxford: Oxford University Press.
MUDAMBI R (1997) A Complete Information Index for Measuring the Proportionality of Electoral Systems. Applied Economics Letters, 4. pp. 101-104.
MUDAMBI R, Navarra P and Sobbrio G (2001) Rules, Choices and Strategy: The Political Economy of Italian Electoral Reform. Cheltenham: Edward Elgar.
ORTONA G (1998) Come funzionano i sistemi elettorali: un confronto sperimentale. Stato e mercato, 54. pp. 83-112.
ORTONA G (2000), "A weighted-voting electoral system that performs quite well", in Dardanoni V and Sobbrio G (eds.), Istituzioni politiche e finanza pubblica, Angeli, Milano; also as a working paper, Dep. of Public Choice, Università del Piemonte Orientale, 4 (1999).
ORTONA G (2002a) "Experimental Assessment of a suggested two-stage electoral system", Paper presented to the 2002 Conference of the European Public Choice Society, Belgirate (Italy), April.
ORTONA G (2002b) "Choosing the electoral system: why not simply the best one?" Working Paper, Department of Public Choice, Università del Piemonte Orientale, 32.
SHUGART M S (2001) Electoral "efficiency" and the move to mixed-member systems. Electoral Studies, 20. pp. 173-193.
SHUGART M S and Wattenberg M P Eds. (2000) Mixed-member Electoral Systems: the Best of Both Worlds? Oxford: Oxford University Press.
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