Anything You Have the Votes to Get
23
In the end, the strategic game played under the conditions of the structural theory, generates two suggestive
results. First, precise anticipation precludes some choices. For example, a member has no incentive to vote against after
initially committing for, even though the game structure would allow it as logically possible. Likewise, when the
member initially commits for, the president has no need to consider ‘conceding,’ even though that too the game allows
as a logical possibility. Second and most importantly, precise anticipation generates an equilibrium with simplistic
features: the president will concede only when that concession will result in changing the hesitant member’s vote from
against to for. Given that the member knows the president has arrived at this deduction, the member will hesitate only
of necessity, to underwrite a conversion. Thus, in the structural world, behavior underscores the important linkage
between what the member signals in the proposal stage and all of the choices either possible or made thereafter.
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Faulty anticipation corrupts that linkage and creates a genuinely strategic variant of the structural theory. A
member may have a hard time mustering congressional coherence and employing the power of votes. And few can see
clearly the President’s vision. For each, the politician’s signals become tradecraft. Their signals suggest something of
their intentions, but far less than their intent. For example, hesitation might convince the president that the member
prefers to vote for the proposal only given some concession (i. e., that —B
m
+C
m
>B
m
>—B
m
—P
m
) when the member actually
prefers the proposal. For the president, the bargaining problem becomes how to discern when hesitation necessitates
haggling and when it does not. With only one opportunity to judge the intent of the member, faulty anticipation
hampers the president.
Faulty anticipation also hampers the member who cannot clearly judge what the president will do with different
signals and how much information the president already has about the member’s aims. The member cannot fully
ascertain whether the concession requested would turn the administration from the policy (i. e., whether B
p
>—B
p
>B
p
—
C
p
). So, the member has no straight-forward prediction about what the president will do even when the member
hesitates and, hence, no clear idea about what to signal (to hesitate or to commit).
If the president would concede, the member would hesitate. The president, on the other hand, may suspect that
regardless of a concession, the member would vote for though hesitating initially. The president could then decide not
to concede, even though refusing to grant a favor undoubtedly risks losing the proposal but suggesting that a penalty
would ensue for bluffing. If the president intends to punish when persevering, the member would hesitate only if
willing to vote against. Even in an isolated situation, once only, faulty anticipation makes the game strategic.
To find the bargaining equilibrium, the critical analytic question has to do with the President’s decision whether
to concede or persevere when facing a hesitant member. Since the preceding paragraph suggests that for the President
suspicions play a role in the decisions, call “s” the President’s supposition that a member has dissembled when
hesitating. Define presidential indifference between available options as occurs whenever
Utility
p
(concede) = Utility
p
(persevere). Applying values from Figure 7, this identity becomes [s(Bp — Cp) + (1—s)(Bp —
Cp)] or (Bp — Cp) when conceding and a lottery between a bluffer’s preference for the bill s(Bp) and a genuine
member’s dislike for the bill (1—s)(—Bp) or [s(Bp) + (1—s)(—Bp)]. Manipulating this indifference, (Bp — Cp) = [s(Bp) + (1—
s)(—Bp)], identifies the critical value for the President’s supposition as
p
p
p
s
B
2
C
B
2
−
=
. So, the President perseveres
whenever
p
p
s
B
2
C
1
−
≥
and concedes otherwise.
This simple analysis of the President’s supposition, therefore, rests on the costs of concessions and the benefits
secured. The higher up the administration’s agenda, the fraction becomes smaller and s approaches 1: to persevere the
president must have a very high expectation that the member dissembles when hesitating. Otherwise, the president
will likely concede when facing hesitation. On a critical agenda item, the president needs a very solid case against a
member before risking the consequences of persevering. On the other hand, as the cost of concessions grows, the
Convention