Sunday, May 03, 2009

The VP and the Power of Tie Breaking

In a recent online exchange, a poster trying to defend Biden's mistaken claim that Article I of the Constitution put the VP in the executive branch argued that the VP's role in the Senate, which is what Article I actually describes, is a trivial one, since all he gets to do is to chair the Senate and break ties, and that giving him a trivial role in the legislative branch impled that his real role was in the executive. That started me thinking about tie breaking.

On the face of it, the power to break a tie isn't worth much, since votes are rarely ties. But that way of looking at it is misleading. An ordinary vote is only decisive, after all, if it either breaks a tie or creates one, which is also, in most contexts, a rare situation. The question is how much less power a vote that can be used only to break a tie provides.

Consider a motion in an assembly. For simplicity assume that, absent my vote, the probabilities that the motion will fail by one vote, tie, or pass by one vote—the situations in which my vote might affect the outcome—are equal. Call the common probability p. Assume there is a chairman with the power to break ties, and assume, again for simplicity, that he is equally likely to vote either way on the motion and never abstains. Finally, assume that I want the motion to pass.

If without my vote the motion would fail by one, then I can vote for it and make it a tie. That affects the outcome only if the tie breaker also votes for it. So the probability that I will be able to make it pass by making it into a tie is p/2. If without my vote it would be a tie, then I can vote for it making it pass, but that only affects the outcome if the tie breaker would not have himself voted for it. That gives us another probability of p/2. If without my vote it would pass by one, then my support is not needed and has no effect on the outcome. So the total probability that my support for the bill will affect the outcome is p.

What about the situation from the point of view of the tie breaker? Assuming that a motion fails on a tied vote, he can only affect the outcome if the vote is a tie and he supports the motion. Probability p/2.

What this simple analysis suggests is that the voting power of the VP, if he chooses to exercise it, is half that of an ordinary senator. Whether that plus chairing the Senate, as I gather VP's used to routinely do before LBJ, adds up to more or less than the equivalent of one senator is a question I will leave to others who know more about the subject.

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5 Comments:

At 1:37 PM, May 03, 2009, Anonymous Anonymous said...

Suppose the VP votes whenever he feels like voting. The result (pass/fail) is recorded. This is the "before" result. Then the vote of the VP is subtracted unless it was a tie-breaker. That is, the vote of the VP is left in if the result is tie+1, and subtracted otherwise. The result (pass/fail) is recorded again. This is the "after" result.

The "before" result and the "after" result are identical - i.e., "pass" before is "pass" after, and "fail" before is "fail" after. From this, it appears that there is no difference between counting the VP's vote only when it is a tie-breaker, and counting the VP's vote always. From this it appears that the VP has the same power to affect the result as any senator.

 
At 1:44 PM, May 03, 2009, Anonymous Anonymous said...

The original argument is right under assumption that a senator voting/not voting decision is done only on a pivotal basis.

Since senate's votes are a public record, this assumption is arguably less true than for citizens. Non-pivotal citizen's vote does not offer external value. However, a senator can use both pivotal and non-pivotal votes to signal his ideology to external observers (parties, electorate). Besides signalling his positions, senator also signals his "participation" in the democratic process (here I am, "working", exerting "effort" -- my salary is not wasted).

If the VP votes rarely (some data would be nice), then he has less claim to being paid for the mere possibility of exerting effort (presumably, learning the issue, forming a position).

 
At 2:39 PM, May 03, 2009, Blogger blink said...

Your analysis of tie-break voting is correct, but applying it to the Senate missing important features. For example, cloture votes do not depend on the 51st vote in favor, but the 60th, and these votes may be more important than the actual votes on legislation. Moreover, to the extent that important work is done in committees writing, crafting, and framing bills, the Vice President’s tie breaker role does not come into play.

 
At 8:32 AM, May 05, 2009, Blogger dWj said...

I came here more or less to write what blink wrote, but will instead point out to the first anonymous that if the VP, by voting, would create a tie, that vote does not count. That's the big difference between his vote and that of a Senator.

Back to blink: I expect the ability to propose legislation, sit on committees, and even debate are worth more than chairing the Senate. If he has gained influence on the Senate since last October, then Obama has gained more influence on the Senate since last October; informal influence is the only way in which I can imagine a VP being worth more than a Senator in the Senate.

 
At 2:02 AM, May 08, 2009, Anonymous Anonymous said...

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