13th August, 2019
My first exposure to economic research was through Prof. Timan Börgers while doing Honors in the University of Michigan. Through his guidance, I studied how to model voting behavior, and wrote a rough draft comparing simultaneous and sequential voting model. Framework for simultaneous and sequential voting is designed to model the voting system in the House of Representatives and the Senate respectively. At the point of writing the draft, I wasn't aware that similar work has already been done. However, upon browsing through more literature, I have come to realization to Groceclose and Milyo (2010) has written a paper on essentially the same topic, in a more fashionable manner. Contents for this blog post is derived heavily from the works of Groseclose and Milyo (2010), though I have added a slightly different interpretation and discussion at the end.
While the House decides on an uncontested issues through non-recorded votes such as voice votes or division votes, the legislators may demand for a recorded vote or Yea-and-Nay vote on controversial issues. The recorded votes are usually held electronically for a fixed amount of time (usually for at least fifteen minutes), with the representatives' vote displayed in the two summary panels. Representatives are free to change their votes in the first ten minutes freely, and in the last five minutes they can use a teller card to change their votes (For more details, see Chapter 58 on Johnson, Sullivan and Wickham, 2017).
Now, to model the aforementioned voting model in the House, I first assumed that the members have two types of preference:
To formally characterize this, let the utility function of the member be:
ui(x, y) = oi(x) + pi(y),
where x is the winning alternative, y is the alternative that the member i voted for, and oi and pi each indicates the outcome preference and position-taking preference respectively.
In many cases, outcome preferences are aligned with position-taking preference. If member A belongs to Democratic party, it makes sense that A has similar ideological preference to that of Democratic party. Let's call the members whose outcome preferences and position-taking preferences are aligned dominant agents.
However, while member A's ideological point may be closer to that of Democratic party than of Republican party, member A may disagree with Democratic party on some topics. For example, let's say that member A is voting between a and b. Member A personally likes alternative a, but her party prefers b. If possible, when her vote does not switch the result of the bill, in another word when she is not pivotal, she would vote for alternative a. When the bill is losing by just one margin, or when she is pivotal, A would rather have her party win, and vote for b. Let's call these members conflicted agents.
In addition, there may be a somewhat confused member. Let's say member B really hates b, even though her party prefers b. However, because member B hates b so much that she would vote for a even though her vote may cause her party to lose. Perhaps she should rather belong to other party, but she just feels strongly about this particular issue. On other issues, she may be happy with the ideological platform of her party. Let's call these members confused agents.
To simplify the notation, let's normalize pi(b) = 0. Note that if the member prefers a, then pi(a) > 0 and if the member prefers b, then pi(a) < 0. Without loss of generality, let us now consider member i who belongs to the party that prefers a. Then member i is the following agents if:
It's easy to guess what dominant agents or confused agents would vote. They will simply vote for their position-taking preference. However, for conflicted agents, decision gets a little more sophisticated. When the agent is not pivotal, then she will vote according to her position-taking preference, but she will vote according to her outcome preference if she is pivotal.
With an additional (hopefully harmless) assumption, we are ready to prove the result mentioned in the title of this blog.
Assumption 1: There exists at least one conflicted agents on both parties.
This assumption is reasonable when dealing with controversial issues, with 435 members in the House of Representatives.
Now to prove the main result:
Proposition 1: If an equilibrium exists, then all the legislators vote according to their position-taking preference.
Proof: Let's prove the proposition by contradiction. Assume that an equilibrium exists, and at least one legislator vote according her outcome preference. Note that it is optimal for all dominant agents and confused agents to vote according to their position-taking preference. Hence only conflicted agents will vote according to their outcome preference.
Without loss of generality, let's assume that a was the winning alternative. Let agent i be the conflicted agent who has voted according to her outcome preference. Let us also assume that agent i prefers a but whose party prefers b. Note that agent i exists due to our initial assumption. Since agent i voted according to her outcome preference, she must have voted for b. However, since a won, she must not be pivotal. However, conflicted agents vote according to their position-taking preference when they are not pivotal, hence contradiction.
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This result suggests that all legislators in the House vote as if they do not really care about the outcome. Rather, they make their voting decision based on the act of voting itself. Groseclose and Milyo (2010) describes such phenomenon as sincere voting' In the simultaneous voting model, they define sincere voting as voting according to the position-taking preference, while they define sophisticated voting as voting according to outcome preference when outcome preference and position-taking preference differs. However, as Denzau, Riker and Shepsle (1985) argue, this terminology could be a misnomer. While all agents will vote according to their position-taking preference in the equilibrium, they need not be "naive", "myopic" or "sincere". Rather, this nonstrategic voting, like sophisticated voting, is a product of rationality and maximization of utility.
It is also important to note that the aforementioned model only really applies to voting in the House. In the Senate, voting is held sequentially, according to the order of the Senators' last name. When the Senators are voting sequentially, this result no longer holds. Instead, both Spenkuch, Montagnes and Magleby (2018) and Groseclose and Milyo (2013) observed the evidence of strategic voting when looking at the roll-call votes of the Senate.
Another caveat that we must consider is the effect of party affiliation on the House members. In the beginning of this article, we first ascribed party affiliation as a major source of outcome preference. Indeed, Spenkuch, Montagnes and Magleby (2018) described this outcome preference as "concerns about their party's reputation or brand", or "pressures from party elites on rank and file members". At first glance, since no members vote according to their outcome preference, naturally party affiliation should have no effect on the voting behavior in the House. However, Snyder and Groseclose (2000) have discovered strong evidence of party influence in both the House and the Senate in virtually all congresses.
All these contradicting evidences seem to point out that either legislators are not voting in the equilibrium, or our initial understanding of the party affiliation may be wrong. Groseclose and Milyo (2010) argues that "no-quick-gavel" policy in the House, which allows legislators to change their votes after seeing the votes of their colleagues, implies that the voting behavior should be consistent with the equilibrium, if they are voting rationally. While this assumption could be wrong, we could also consider the case where party affiliation affects both the outcome preference and the position-taking preference. It may be true that the party suffers a penalty if they lose an important bill, perhaps through losing trust from their electorates. However, party elites or party supporters in the general public may also condemn the deviation from party line, even if the party wins the bill. Indeed, Snyder and Groseclose (2000) have constructed their model assuming that party affiliation affects their position-taking utility.
Regardless of whether party affiliation affects the voting behavior of the House through outcome preference or through position-taking preference, one thing is sure from this result. Rewarding or punishing the House members for winning or losing the bill will not have much impact on their voting behavior. Rather, rewarding or punishing the legislators for their votes, irregardless of the outcome, should have a much stronger influence.
Denzau, A., Riker, W., and Shepsle, K. (1985). "Farquharson and Fenno: Sophisticated Voting and Home Style". The American Political Science Review, 79(4): 1117-1134.
Groseclose, T., and Milyo J. (2010). "Sincere versus Sophisticated Voting in Congress: Theory and Evidence". The Journal of Politics, 72(1): 60-73.
Groseclose, T., and Milyo J. (2013). "Sincere versus Sophisticated Voting when Legislators vote Sequentially". Social Choice and Welfare, 40(3): 745-751.
Groseclose T., and Snyder, J. M. Jr. (2000). "Estimating Party Influence in Congressional Roll-Call Voting" American Journal of Political Science, 44(2): 193-211.
Johnson, C. W., Sullivan, J. V., and Wickham, T. J. Jr. (2017). "House Practice: A Guide to the Rules, Precedents and Procedures of the House". U.S. Government Publishing Office, Congressional Rules and Procedures, 115th Congress, 1st Session.
Spenkuch, J. L., Montagnes, B. P., and Magleby, D. B. (2018). "Backward Induction in the Wild? Evidence from Sequential Voting in the U.S. Senate". American Economic Review, 108(7): 1971-2013.