CONNECTICUT AS A PIVOTAL STATE

Part of the reason that Sherman was effective may have been that his state, Connecticut, was pivotal on many votes. This can be shown by estimating ideal points for the twelve states that attended the Convention. For this purpose we use Poole's (2000) optimal classification routine.³

Optimal classification unfolds binary data by first estimating an optimal cutting plane for each vote, then optimally classifying voters in the regions formed by these planes. It is particularly useful for samples with missing data and settings where minimal restrictions are desired. Optimal classification assumes that all delegates vote sincerely in Euclidean space with symmetric single-peak preferences containing fixed ideal points. Although most of these assumptions are standard for spatial estimation (e.g., NOMINATE scores), we explicitly defend their legitimacy in the context of the Constitutional Convention in the Appendix.

Optimal classification estimates for the 569 state-level roll call votes at the Convention are displayed in Figure 1 (see Jillson 1988, 215–20, for the data).⁴

These results were generated by restricting New Jersey in the first dimension and Pennsylvania in the second dimension. However, the same mapping of ideal points (or a mirror image of that mapping) was produced regardless of which states were restricted. Figure 1 is also consistent with the Bayesian estimates of Pope and Treier (2004) and more loosely with the factor analyses of Jillson (1988). This suggests that the ideal points displayed in Figure 1 are robust.⁵

The two dimensions in Figure 1 are empirically derived. Hence, they are linear transformations, or near linear transformations, of a wide variety of issues. Although it is merely speculative, the distribution of states across the first dimension appears to correlate with the coalitions formed over issues of representation (Jillson 1988; Robertson 2005),⁶

and the distribution of states across the second dimension appears to correlate with the coalitions formed over issues of centralization (Jillson 1988).

Rhode Island never attended the Convention, hence, it is not included in Figure 1. Moreover, delegates from New York and New Hampshire never attended at the same time. To account for the differing attendance of these two states, we divide the Convention into three periods: May 30 to July 10 (when New York attends, but New Hampshire does not), July 11 to July 22, (when neither state attends),⁷

and July 23-Sept 17 (when New Hampshire attends, but New York does not).

During the first period (May 30–July 10), Pennsylvania is the median state in the first dimension and Connecticut is the median state in the second dimension. During the second period (July 11–July 22), both Pennsylvania and Virginia are the median states in the first dimension (an even number of states imply at least two states at the median), and Connecticut and Maryland are the median states in the second dimension. During the third period, Virginia is the median in the first dimension and Connecticut is the median in the second dimension.

Without knowing the location of the status quo and the proposal for any particular vote, we cannot determine pivotalness based on medians. Instead, we calculate Shapley–Owen values (Owen and Shapley 1989) for the states using the ideal points estimated in Figure 1.⁸

A Shapley–Owen value measures the percentage of all possible minimum winning coalitions in which a state is a member. In other words, it measures how often a state is pivotal for all possible votes. Although power indices, like Shapley–Owen values, are good descriptions of an actor's chances of affecting the outcome a priori, they are not intended to evaluate coalitions that actually formed around specific clauses (Riker and Ordeshook 1973). In this sense, power indices may provide accurate predictions of overall performance (such as an actor's effectiveness across the course of the Convention) but they do not predict an actor's effectiveness on any single vote.

Calculating Shapley–Owen values for the states, we found that Connecticut had the largest Shapley–Owen value during each of the three periods. During the first period, the three largest Shapley–Owen values were Connecticut (.40), Georgia (.17), and Pennsylvania (.13). During the second period, the three largest were Connecticut (.30), Virginia (.27), and South Carolina (.17). During the third period, the three largest were Connecticut (.33), Virginia (.23), and New Hampshire (.17). Connecticut's vote was not pivotal on every single issue, but the power index in each period suggests that it was more likely to be critical to the final vote tally than any other state a priori. This implies that, everything else equal, the delegates from Connecticut had greater influence on the Constitution than delegates from states like New Jersey, which were rarely in a position to affect the outcome of a vote.

A PIVOTAL DELEGATE FROM CONNECTICUT

Not only was Connecticut likely to be pivotal, as suggested in the previous section, but also it appears that Sherman was the most pivotal delegate from his state. Delegate level votes were not recorded at the Convention. However, McDonald (1958) inferred sixteen delegate level votes using delegate positions in speeches and manuscripts. He then compared these positions to attendance records and state votes recorded in the journal to fill in missing values. His data have been used extensively by McGuire (1988, 2003) and McGuire and Ohsfeldt (1986). Using the same process as McDonald, we were able to infer an additional sixteen votes for the three Connecticut delegates. For example, Ellsworth is coded as voting yea on vote 249 because he made the motion. Johnson and Sherman are coded as nay on vote 249 because Connecticut voted nay and a majority of each delegation determined the vote of their state. Combined, these 32 votes spanned all 5 months of the Convention but focused primarily on cases where all three delegates were in attendance (June 2–August 23). The votes represent a wide range of issues from the apportionment of the legislature and election of the President to the powers of issuing currency and the importation of slaves. We then used these 32 votes to create optimal classification estimates for the Connecticut delegation.⁹

Although two dimensions are more compatible with our analysis, we assumed one dimension because only one dimension could be meaningfully recovered for three voters. We found that in a single dimension Sherman was the median of the three delegates from Connecticut.¹⁰ This suggests he was the most pivotal delegate from his state.

After August 23, when Ellsworth left the Convention, Sherman and Johnson were the only delegates remaining from Connecticut. By definition, both delegates were equally pivotal in determining Connecticut's vote during this period. Prior to August 23, Sherman was the median voter in our single-dimensional estimates. This is true whether ideal points are estimated from all 32 recovered votes or from only the 21 votes which took place through August 23. Although it is always possible that recovering additional votes might produce different conclusions, the available evidence suggests that Sherman was the most pivotal delegate from his state.

Our analysis suggests that Sherman was in a better position to affect the outcome of the Convention than other delegates due to his ideological position. His state was critical to the outcome on many issues. When all three Connecticut delegates were present, Sherman fell between the positions of his two co-delegates, making his vote frequently critical. When only one other Connecticut delegate attended, Sherman (and Johnson) could always alter his state's vote. Hence, part of Sherman's effectiveness at the Convention might stem from his spatial position relative to others and the rule requiring delegates to vote in state blocks.

NONPIVOTAL AMONG DELEGATES ALONE

Sherman's ability to influence the content of the Constitution may have resulted in part from the voting rules themselves. If the Convention rules had differed, such that passage of a proposal required a simple majority of all delegates voting individually (as done in the modern-day House), then Sherman might have been less pivotal. This is revealed by creating optimal classification estimates for 53 of the 55 delegates at the Convention,¹¹

using the 16 roll-call votes coded in McGuire (2003).¹² Given this limited sample of votes, our analysis in this section can only be considered suggestive but it does support our contention that the rules were important.

Under the assumption of a single dimension, one of two orderings are created—depending on the restriction. Either C. C. Pinckney (SC), Rutledge (SC), and Butler (SC) are at the median (they have the same estimated ideal point), or Spaight (NC), Davie (NC), and Pierce (GA) are at the median (they have same estimated ideal point). This is true for all three periods of attendance. Sherman is in 45th position in the first series of estimates, and in the 10th position in the second series. In either case, there are at least 14 delegates between Sherman and the median voter. In other words, Sherman would be far from pivotal in the single-dimensional case.

With only 16 votes for each delegate, two-dimensional estimates are very imprecise, and delegate restrictions have noticeable effects on the spatial mappings. Nevertheless, Sherman is not a centrist in two dimensions. Investigating more than 35 combinations of restrictions, we found that there were no fewer than 8 delegates between Sherman and the median in the first dimension and no fewer than 14 delegates between Sherman and the median in the second dimension—across all three periods of attendance. Typically, Sherman was estimated to be more extreme. In the case where Sherman was the most centrist, 12 other delegates had greater Shapley–Owen values than Sherman—the top 5 of which were from the South (Pierce, Spaight, Baldwin, C. C. Pinckney, and Rutledge). Combined with the single-dimensional results, this suggests that Sherman was unlikely to have been pivotal if votes were tallied by individuals.

If the votes were tallied individually, rather than by state, then Sherman might have been less effective. Under this counterfactual, Southern delegates would have been in the most pivotal positions, and the Constitution might have been a very different document. With slavery and the regulation of international trade at stake, the method of tallying votes might have had a significant effect on the nation's political development. However, given the limited data, we again stress that the results in this section are merely suggestive.

A COMPARISON OF THE PERSONAL POWER AND SPATIAL PIVOT ARGUMENTS

Although Rakove (1996) and Robertson (2005) claimed that Sherman's effectiveness was due to various types of personal power, our analysis suggests that Sherman's spatial position, and the spatial position of his state, could also explain his overall effectiveness. Because both arguments can explain the same phenomena, and one argument need not preclude the other, it may be difficult to assess their relative contributions. Nevertheless, in this section, we try to do just that. We highlight two pieces of evidence that shed some light on the relative merits of the personal power and pivotal voter arguments.

Personal power can be exercised in many forms. One form is the ability to propose motions that pass. Success rates on motions capture the ability to forward an agenda or to counter another delegate by alternative phrasing—as Robertson claimed was the intent of Sherman. Some of the most capable delegates in this regard were Edmund Randolph, James Wilson, Gouverneur Morris, and Elbridge Gerry. Each of these delegates made more than 20 motions at the Convention and passed their motions at above-average rates (see Table 1).¹³

Sherman and Madison made more than 15 motions each, but they succeeded at below-average rates—33% and 37%, respectively. This suggests that neither Sherman nor Madison was particularly skilled at crafting successful motions. They may have influenced the Convention in other ways, but they did not demonstrate this type of personal power.¹⁴

Alternatively, personal power may manifest itself through a delegate's ability to block proposals made by other delegates. According to Robertson (2005) and Rakove (1996), Sherman was particularly good at obstructing Madison. This type of personal power is more difficult to evaluate because no one motions an opposition. Delegates can take stances in opposition, but the causal connection between one delegate stating a position and another delegate changing his vote is always tenuous—particularly for a small number of cases. There are times when a delegate might have vocalized his opposition to an issue followed by another delegate changing his stance on the issue. Such observations are consistent with a story of personal power, but other explanations are still plausible. For example, the new stance could be due to subtle changes in the phrasing of the question, fatigue, or a variety of other factors.

To more directly assess the affect of Sherman's personal power and his pivotalness on his overall effectiveness, we need to find a situation where their predictions differ. In a biography of Sherman, Collier (1971, 316) seems to claim that Sherman was less influential in the First Federal House than he was at the Federal Convention. This is interesting because the method of tallying votes differed between the two bodies (as noted previously, votes were tallied by individuals in the House; they were tallied by states at the Convention) and because the House contained different personages than the Convention. These differences could affect Sherman's pivotalness, but they should not reduce the effectiveness of his intrinsic qualities. If personal power is about Sherman's intrinsic qualities in and of themselves, not about his qualities relative to others, then there should be no change in Sherman's personal power between the two bodies. If personal power is about Sherman's intrinsic qualities relative to others, and these qualities correlate with political experience, then we should expect Sherman to have greater personal power in the House than at the Convention. The House contained a smaller percentage of experienced statesmen than the Convention; hence we would expect Sherman to have greater personal power relative to others there. However, both claims about personal power contradict Collier's observation that Sherman was less influential in the House.

The pivotal voter argument does a better job of explaining Collier's observation. If the pivotal voter argument is correct, Sherman should be more influential where he was more pivotal. Using Lewis and Poole's two-dimensional W-NOMINATE scores for the First Federal House,¹⁵

we calculated Sherman's Shapley–Owen value in two dimensional space as less than 5×10⁻⁴. This Shapley–Owen value is smaller than the values of 25 of the other 65 representatives, suggesting that Sherman was less pivotal in the House than he was at the Convention. Perhaps Sherman was less effective in the House because, on average, he was in a worse position to affect the outcome. Without maintaining a favorable position relative to others under the established voting rules, someone who was effective in one setting was less effective in another.