Judges’ Law: Ideology and Coalition in Mexico’s Electoral Tribunal∗ Federico Est´evez ITAM
Eric Magar ITAM
[email protected]
[email protected]
6 November, 2008
Abstract We report work in progress. The paper investigates the voting records of members of Mexico’s Federal Election Tribunal (TRIFE) between 1996 and 2006. We employ Markov Chain Monte Carlo methods to fit a Bayesian measurement model of ideal points for eight judges’ who served in the period. Our results show that, even if judges seldom vote divided, systematic cleavages appear when they do. Judges have policy preferences spreading them along an ideological space roughly in three groups.
Courts have immense power. The unelected branch of democracies does policy by interpreting the constitution. And even if, unlike the other branches of government, the judiciary is only reactive, the decisions it reaches can have immense consequences (eg. McCubbins and Lax 2006). We inspect voting patterns in Mexico’s Tribunal Electoral del Poder Judicial de la Federaci´on (TRIFE) between 20 December 1996 and 7 December 2006. TRIFE is a 7-judge, appeals court with authority to pronounce lastinstance rulings on any challenge to decisions by election authorities (both at the state and federal levels) and parties themselves. We use Markov Chain Monte Carlo methods to estimate judge’s policy preferences from their voting profiles in cases that were not decided unanimously via Bayesian simulation. Estimation reveals systematic differences between judges’ preferences. We also investigate judge consistency across types of cases, finding that judges (especially two of them) aligned differently in rulings involving challenges to the election authority and rulings about state elections and citizen rights. The paper reports preliminary results and proceeds as follows. In section 1 we (will) discuss TRIFE’s institutional structure. Section 2 describes the ∗
Paper prepared for the Bayesian Methods in Social Sciences seminar, CIDE Mexico City, 6–7 November, 2008. We are grateful to Guillermo Rosas for invaluable help with methods, and to Francisco Cant´ u, Elisa Lavore, and Gustavo Robles for research assistance. Errors remaining are the sole responsibility of the authors.
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votes in the dataset, comparing them to the unanimous ones that are left out. Section 3 derives the spatial model that underlies ideology scaling methods and the Bayesian specification of the model to be estimated. Section 4 presents the results, showing that there are systematic policy differences between judges despite the very high degree of consensual rulings. We compare estimates based on all votes with those based on subsets of votes, showing which judges are more and which less consistent. Section 5 concludes.
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TRIFE: appointment, procedure, etc.
Forthcoming... Judge De la Peza died in office in January 2005 and was replaced. We considered the periods before and after his death jointly and in isolation, in order to check for differences. Period 1 runs from December 1996 to December 2004, inclusive. Period 2 runs from January 2005 to December 2006, inclusive. Judges in period 1 were Castillo, De la Peza, Fuentes, Navarro, Ojesto, Orozco, and Reyes. Judge Luna filled the vacancy in period 2.
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The votes behind the rulings
On any issue put to a vote, judges can vote aye or nay and are not allowed to abstain, although they are often absent from the session (0.35 member was absent from the session on average in period 1; 0.82 in period 2, due to the four-month vacancy before Judge Luna was appointed). Since we are attempting to infer judges’ preferences from their voting record, only items that were not ruled unanimously provide any information. So all noncontested votes (defined as a vote where no judge voted aye or no judge voted nay) were dropped from analysis. This left us with 66 votes out of 1,264, or slightly more than 5%. Table 1 lists their breakdown by vote type, distinguishing challenges to IFE decisions (IFE is the federal election regulatory agency, see Est´evez, Magar and Rosas 2008), disputes between parties and their rank-and-file (broadly labeled citizen rights), issues arising from state and municipal elections, and a residual category. 57 contested votes took place before Judge De la Peza’s death, only 9 afterwards. Vote type unanimous contested Total IFE 584 40 624 citizen 463 22 485 states 119 4 123 other 32 0 32 Total 1,198 66 1,264
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| Contested vote Vote type | 0 1 | Total ---------------+----------------------+---------IFE challenge | 584 40 | 624 | 93.59 6.41 | 100.00 ---------------+----------------------+---------Citizen right | 463 22 | 485 | 95.46 4.54 | 100.00 ---------------+----------------------+---------State election| 119 4 | 123 | 96.75 3.25 | 100.00 ---------------+----------------------+---------Other | 32 0 | 32 | 100.00 0.00 | 100.00 ---------------+----------------------+---------Total | 1,198 66 | 1,264 | 94.78 5.22 | 100.00 Period | 0 1 | Total ---------------+----------------------+---------1 (1996-2004) | 811 57 | 868 2 (2005-2006) | 387 9 | 396 ---------------+----------------------+---------Total | 1,198 66 | 1,264
Table 1: Contested votes by type and period
Type IFE (RAP+RRV) citizen rights (JDC) state elections (JRC) various constitutional (AES) other (JIN) other (REC) Total
sample 624 485 123 32 0 0 1,264
all 689 6145 3955 252 583 250 11,874
% 91 8 3 13 0 0 11
Table 2: Case selection 1996–2006: sample and universe by vote type
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Vote type
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IFE citizen states other Total
68 28 65 0 51
IFE citizen states other Total
63 36 50 — 53
Ruling reject dismiss other Unanimous votes 10 22 <1 16 45 11 15 20 0 0 100 0 12 33 5 Contested votes 20 15 3 23 41 0 50 0 0 — — — 23 23 2
Total 100 100 100 100 100 100 100 100 — 100
Model specification
Scaling techniques to infer ideology rely on a standard spatial model of voting (Hotelling 1929, Poole and Rosenthal 1997). The approach assumes that policy and ideology can be mapped in the same space, and that distance determines utility and voting. Judges in this context differ from one another in their locations in the policy space, each voting for the alternative closer to his or her ideal point. The aim is to use judges’ observed votes in order to estimate their ideal points and other parameters of interest. We specified one- and two-dimensional versions of the model. The key assumption of the spatial approach is that voting ‘aye’ (y = 1) or ‘nay’ (y = 0) on an issue depends on the relative locations of policy outcomes vis-`a-vis judge j’s ideal point xj in space. Voting is sincere. If x(A) , x(N ) ∈ R (we later discuss the 2D version) denote the outcomes of the aye and the (A) (N ) nay votes, respectively, it is their midpoint m = x +x that matters for 2 analysis. The judge will prefer the alternative falling on the same side of m as his or her ideal point (for a review, see Rosenthal 1990). Formally, j’s vote propensity yj∗ is yj∗ = xj − m + error
(1)
where xj is judge j’s ideal point and the voting rule is yj = 1 ⇐⇒ yj∗ ≥ 0, otherwise yj = 0. The model becomes item-response-equivalent (see Gelman and Hill 2007)1 by multiplying the utility differential by a weight δ ∈ R , leaving the equation as 1
Item-response models are designed to infer a latent trait (eg. intellectual ability or ideology) from allegedly related subjects’ traits (eg. answers to items in the GRE test or roll call votes).
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yj∗ = δ(xj − m) + error.2
(2)
A larger δ (in absolute value) indicates a more polarizing issue, an item discriminating the judges’ ideology better. In the extreme, where δ = 0, the utility differential plays no role and voting is entirely determined by the random disturbance. A negative δ reverses aye and nay votes, letting analysis proceed without requiring an a priori judgement about which vote falls to the left and which to the right of the policy space. The two-dimensional extension is straightforward. Judge j’s ideal point xj ∈ R2 now has two coordinates in space, xj,1 and xj,2 . The same goes for policy. What now matters for voting is the line x2 = ax1 + b cutting space in two sides: all those with ideal points on one side voting aye, the rest nay. This bisector passes through midpoint m and is orthogonal to the line connecting x(A) and x(N ) . Thus defined, all points on one side are closer to x(A) than to x(N ) and therefore vote aye, the rest vote nay. The vote propensity in 2D becomes yj∗ = δ(axj,1 + b − xj,2 ) + error
(3)
where xj,1 and xj,2 are the coordinates of j’s ideal point, a and b are issue parameters that we need to estimate along ideal points.3 Small committees, like TRIFE, raise complications for model estimation (Londregan 2000). With J = 7 judges and I = 57 items (all votes in period 1), J × I = 399 data points are used to estimate 2 × I + J = 129 parameters. With only 3 observations per parameter, likelihood-based estimation becomes problematic. Bayesian estimation can easily overcome such problems, and can be implemented through Markov Chain Monte Carlo techniques (Clinton, Jackman and Rivers 2004, Martin and Quinn 2002).4 The Bayesian approach requires prior probabilities for all parameters to be estimated: xj , mi and δi (i = 1 · · · I and j = 1 · · · J)) in the onedimensional version; xj , ai , bi and δi in two dimensions. We adopted noninformative priors — ie. a zero-mean normal distribution with variance one — for all parameters except two or three judges’ ideal points. These were 2
δ = −2(x(A) − x(N ) ) when relying on quadratic utility functions. Estimation does not recover the coordinates of the aye and nay policy alternatives, only their midpoint. As the distance between them increases, their choice becomes likelier to arouse passions between judges, which is precisely what δ is intended to capture. 3 We note that the 2D model becomes indeterminate if the bisector lines is perfectly vertical to the X axis (ie. a → ∞). This occurs when no variance is observed in the second dimension and ideal points line-up perfectly in the first (ie. when a second dimension is being forced when none in fact exists). To avoid this problem, we rely on priors that locate the extreme anchors in the first dimension in the first and thirds quadrants (they draw a 45-degree line). If the empirical pattern collapses ideal point parameters to a single dimension, the resulting bisector will be a 135-degree line, not the indeterminate 90-degree line. 4 We estimated the models with WinBUGS software (www.mrc-bsu.cam.ac.uk/bugs) running it from R (www.r-project.org).
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Inference for Bugs model at "model8.txt", fit using WinBUGS, 3 chains, each with 20000 iterations (first 10000 discarded), n.thin = 10 n.sims = 3000 iterations saved Post. Post. Post. Credible interval median mean sd 2.5% 97.5% Rhat n.eff Reyes -1.584 -1.587 0.32 -2.238 -0.981 1 3000 Castillo -1.436 -1.442 0.35 -2.169 -0.794 1 3000 De la Peza -0.219 -0.219 0.29 -0.810 0.344 1 1500 Luna -0.180 -0.168 0.66 -1.400 1.104 1 600 Orozco -0.084 -0.078 0.29 -0.629 0.481 1 1300 Ojesto -0.032 -0.028 0.29 -0.602 0.544 1 3000 Navarro 0.524 0.527 0.29 -0.026 1.102 1 3000 Fuentes 1.556 1.566 0.31 0.964 2.200 1 3000
Table 3: Posterior density summary of ideal points of TRIFE Judges, all votes 1996–2006 instead given semi-informative priors so as to solve the scale and rotational invariance problems (ie. give the arbitrary scale on which estimates are mapped a unit and a sense of what “right” and “left” actually mean). In the one-dimensional version, Judge Fuentes, who dealt with a larger number of PRI-related cases than the rest, was placed towards the right and Judge Reyes, who voted with Fuentes least often, towards the left. In the twodimensional version, Fuentes was located in the first quadrant, Reyes in the third (anchoring a diagonal left-right dimension), while Judge De la Peza was situated in the fourth quadrant, anchoring the second dimension. Formally, the semi-informative priors used were the following: Judge Fuentes Reyes De la Peza
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1-dimension priors xj ∼ N (2, .25) xj ∼ N (−2, .25) xj ∼ N (0, 1)
2-dimension priors xj ∼ N ([2, 2], [.25, .25]) xj ∼ N ([−2, −2], [.25, .25]) xj ∼ N ([−2, 2], [.25, .25])
Results
Estimation proceeded by updating the model thousands of times, then taking a sample of posterior parameter simulations for analysis.5 One-dimension ideal point parameter estimates for all votes in the two periods pooled together appears in Table 3. The median of the posterior density for each judge’s ideal point xj can be taken as a point prediction. This rank judges, from left to right, in the following order: Reyes, Castillo, De la Peza, Luna, Orozco, Ojesto, Navarro, and Fuentes. Those located in the extremes of the spectrum by the prior 5 Three chains were updated 20 thousand times each. The first 10 thousand burn-in scans for each chain were dropped, retaining every tenth simulation of the remainder. This ˆ ≈ 1, produced a sample of 3 × 1000 = 3000 posterior simulations. Gelman and Hill’s R suggesting that the chains had converged towards a steady state.
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Figure 1: Judges’ ideal points 1996–2006. Medians and 80% intervals of posterior estimates
assumptions remained so; the rest had been bunched at the middle, and model updating spread them between the extremes. Figure 1 portrays point estimates surrounded by 80% highest probability density (HPD) intervals to see estimation error. The figure portrays TRIFE cleavages neatly. Judges closer to/farther from each other are more/less likely to vote the same way on a randomly chosen vote. Three voting blocs are discernible: Judges Reyes and Castillo represent TRIFE’s left; De la Peza, Orozco, and Ojesto the center; and Fuentes the right, with Navarro connecting the center and right. The estimate for Judge Luna, who replaced De la Peza, is based of few votes and does not give much information to shift him from the N(0,1) prior probability from which he starts the iteration process. A preliminary qualitative inspection of vote content suggests that the inferred spectrum represents a party leaders v. IFE divide — the regulated against the regulator — left’ judges voting to uphold decisions that the parties object, ‘right’ ones protecting party leaderships. We also estimated the model for periods 1 and 2 separately, although more than 85% of contested votes fall in the former. As one would expect, Figure 2 shows that the 9 votes in period 2 offer scant leverage to update 7
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prior probabilities (judges remain very close to where they started). Period 1 estimates closely resemble those reported in Figure 1 for votes in the two periods pooled together. Inferences of ideology from period 1 only are very close to the pooled ones, but each offer advantages. Period 1 estimates take a real, 7-member panel of judges; the pooled model contrast all 8 judges that ruled in the period we study. Figure 3 gives a neat representation of the model at work. Each panel draws the ideal point estimates for the 7 judges in period 1 along one item’s mi (midpoint) and δi (discrimination factor) parameter estimates. Item 45 in the upper-left panel represents a correct prediction: all judges with ideal points to the left of the midpoint (drawn as a vertical segment on the policy space) were expected to vote one way (and all in fact voted nay), those to the right of m45 the other way (and all voted aye). So this item involves no error, unlike item 33, in the lower-left panel, where we expected Judge Ojesto to vote aye but in fact voted nay. But error is relatively small, as shown by the item’s δ33 close to the median for all items. Item 33 is patently different from item 6 in the upper-right panel, where error overrides the vote propensity scores to such extent that the extreme judges voted together against the center ones, contradicting the spatial voting premises. Since there are more items similar to number 6 (although not too many, otherwise errors in Figure 1 would be larger) we are left wondering if there is not a second dimension of cleavage between judges. Estimates for a 2-dimensional extension of the model are reported in Figure 4. Judges De la Peza and Orozco do, in fact, slightly depart from the 45degree line-up of the other five. But the variance along the second dimension is too shallow to suggest that it really matters. One-dimensional estimates capture most of the variance, much as in the U.S. Congress throughout most
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Figure 3: Judge and item parameter estimates for four votes (period 1 estimates for all votes)
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Figure 5: Judges’ consistency across vote types 1996–2004: TRIFE v IFE votes, intra-party conflict votes, and local elections votes; medians and 80% intervals of posterior estimates. The lower-left panel reports changes in medians in standardized space (see text)
of its long history (Poole and Rosenthal 1997). We also searched for judge consistency across vote types, finding some interesting differences that are reported in Figure 5. The top two and the lower-left panels report estimates for votes on IFE challenges (N = 40), citizen rights votes (N = 22), and state elections votes (N = 4). The lower-right panel summarizes differences in median posterior densities of ideal points in standardized space for convenience.6 Judge Orozco was among those who moved significantly along the spectrum in different vote types: 6
For a given set of results on some subset of votes, we standardized them by subtracting the left end of the leftmost 80% HPD interval from each estimate and then dividing by the right end of the rightmost 80% HPD interval. So 0 corresponds to the left end of the occupied spectrum, 1 to the right.
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Fuentes Navarro Ojesto Orozco De la Peza Castillo Reyes
All votes 0.000 0.004 0.358 0.343 0.295 0.000 0.000
IFE challenges 0.000 0.001 0.010 0.233 0.421 0.303 0.034
Citizen rights 0.000 0.098 0.354 0.043 0.506 0.000 0.000
State elections 0.004 0.184 0.162 0.448 0.184 0.019 0.001
Table 4: Posterior probability of occupying the median position, period 1
towards the left in votes on IFE challenges, towards the right in citizen rights votes, and to the center in state elections votes. Judge De la Peza moved in similar fashion across types, while the others judges are quite consistent. If Judges Reyes, Castillo, Orozco, and De la Peza formed a tight leftist bloc on IFE challenges, Judges Fuentes, De la Peza, Navarro, and Orozco formed a tight rightist bloc on state and municipal elections votes. It is interesting to note that this pair of judges, despite moving along the spectrum with liberty, nonetheless retain high probabilities of being located at the median of the spectrum across vote types (see Table 4).
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Conclusion
Forthcoming...
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Appendix: BUGS code
### model for 7 members ######################################### cat(" model { for (j in 1:J){ ## loop over judges for (i in 1:I){ ## loop over items y.hat[j,i] ~ dbern(p[j,i]) ## p[j,i] <- phi(y.star[j,i]) ## y.star[j,i] ~ dnorm(mu[j,i],1)I(lower.y[j,i],upper.y[j,i]) ## ## ## mu[j,i] <- delta[i]*(x[j] - m[i]) ## }} ## priors x[1] ~ dnorm(0, 1) #Castillo x[2] ~ dnorm(2, 4) #Fuentes x[3:5] ~ dnorm(0, 1) #Navarro, Ojesto, Orozco x[6] ~ dnorm(-2, 4) #Reyes x[7] ~ dnorm(0, 1) #DelaPeza (period 1) or Luna (period 2) for(i in 1:I){ delta[i] ~ dnorm( 0, 0.25)} for(i in 1:I){
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voting rule sets 0
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Figure 6: Prior and posterior densities for midpoints mi , i = 1, . . . , 57 in period 1. Black dots are judges’ ideal points. Tails thin beyond −3 and 3.
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m[i] ~ dnorm( 0, 0.25)} } ", file="model7.txt") ### model for 8 members ######################################### cat(" model { for (j in 1:J){ ## loop over judges for (i in 1:I){ ## loop over items y.hat[j,i] ~ dbern(p[j,i]) ## p[j,i] <- phi(y.star[j,i]) ## y.star[j,i] ~ dnorm(mu[j,i],1)I(lower.y[j,i],upper.y[j,i]) ## mu[j,i] <- delta[i]*(x[j] - m[i]) ## }} ## priors x[1] ~ dnorm(0, 1) #Castillo x[2] ~ dnorm(2, 4) #Fuentes x[3:5] ~ dnorm(0, 1) #Navarro, Ojesto, Orozco x[6] ~ dnorm(-2, 4) #Reyes x[7:8] ~ dnorm(0, 1) #DelaPeza, Luna for(i in 1:I){ delta[i] ~ dnorm( 0, 0.25)} for(i in 1:I){ m[i] ~ dnorm( 0, 0.25)} } ", file="model8.txt") ### 2-dimensional model for 7 members cat(" model { for (j in 1:J){ ## loop over judges for (i in 1:I){ ## loop over items y.hat[j,i] ~ dbern(p[j,i]) p[j,i] <- phi(y.star[j,i]) y.star[j,i] ~ dnorm(mu[j,i],1)I(lower.y[j,i],upper.y[j,i]) mu[j,i] <- delta[i]*(a[i]*x1[j] + b[i] - x2[j]) }} ## priors x1[1] ~ dnorm(0, 1) #Castillo x1[2] ~ dnorm(2, 4) #Fuentes x1[3:5] ~ dnorm(0, 1) #Navarro, Ojesto, Orozco x1[6] ~ dnorm(-2, 4) #Reyes x1[7] ~ dnorm(-2, 4) #DelaPeza (1) or Luna (2) x2[1] ~ dnorm(0, 1) #Castillo x2[2] ~ dnorm(2, 4) #Fuentes x2[3:5] ~ dnorm(0, 1) #Navarro, Ojesto, Orozco x2[6] ~ dnorm(-2, 4) #Reyes x2[7] ~ dnorm(2, 4) #DelaPeza (1) or Luna (2) for(i in 1:I){ delta[i] ~ dnorm( 0, 0.25)} for(i in 1:I){ a[i] ~ dnorm( 1, 0.25) # 45-degree line b[i] ~ dnorm( 0, 0.25)} } ", file="model7_2DB.txt")
## ## ## ##
voting rule sets 0
voting rule sets 0
### Invoking the models from R using R2WinBugs #################### y <- votes lower.y <- ifelse(is.na(y)==TRUE | y== 1, 0, -5) upper.y <- ifelse(is.na(y)==TRUE | y==-1, 0, 5)
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ystar <- matrix (NA, nrow=J, ncol=I) for (j in 1:J){ for (i in 1:I){ ystar[j,i] <- ifelse(y[j,i]==0, 0, ifelse(y[j,i]==1, runif(1), -1*runif(1)))}} trife.data <- list ("J", "I", "lower.y", "upper.y") trife.inits <- function (){ list ( y.star=ystar, delta=rnorm(I), m=rnorm(I))} trife.parameters <- c("delta", "x", "m") trife.all.1 <- bugs (trife.data, trife.inits, trife.parameters, "model7.txt", n.chains=3, n.iter=100, n.thin=10, debug=T, bugs.directory = "c:/Archivos de programa/WinBUGS14/", program = c("WinBUGS"))
References Clinton, Joshua, Simon Jackman and Douglas Rivers. 2004. “Statistical Analysis of Roll Call Data.” American Political Science Review 98(2):355– 70. Est´evez, Federico, Eric Magar and Guillermo Rosas. 2008. “Partisanship in Non-Partisan Electoral Agencies and Democratic Compliance: Evidence from Mexico’s Federal Electoral Institute.” Electoral Studies 27(2):257–71. Gelman, Andrew and Jennifer Hill. 2007. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. Hotelling, Harold. 1929. “Stability in Competition.” The Economic Journal 39:41–57. Londregan, John B. 2000. Legislative Institutions and Ideology in Chile’s Democratic Transition. New York: Cambridge University Press. Martin, Andrew D. and Kevin M. Quinn. 2002. “Dynamic Ideal Point Estimation via Markov Chain Monte Carlo for the U.S. Supreme Court.” Political Analysis 10(2):134–53. McCubbins, Mathew D. and Jeffrey Lax. 2006. “Courts, Congress and Public Policy, Part I: The FDA, the Courts and the Regulation of Tobacco.” Journal of Contemporary Legal Issues 15(1):164–90. Poole, Keith T. and Howard Rosenthal. 1997. Congress: A PoliticalEconomic History of Roll Call Voting. New York: Oxford University Press. Rosenthal, Howard. 1990. The Setter Model. In Advances in the Spatial Theory of Voting, ed. James M. Enelow and Melvin J. Hinich. Cambridge: Cambridge University Press pp. 199–234.
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