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Solutions Manual for Analyzing Politics Rationality, Behavior, and Institutions, 2nd Edition by Kenneth, Shepsle (All Chapters) A+
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Solutions Manual for Analyzing Politics Rationality, Behavior, and Institutions, 2nd Edition by Kenneth, Shepsle (All Chapters) A+..

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  • October 8, 2024
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  • politics
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Solutions Manual for Analyzing Politics Rationality,

Behavior, and Instititutions, 2nd Edition by Kenneth, Shepsle

(All Chapters) A+
Analyzing Politics: Answer Key

Chapter 2: Problems and Discussion Questions

4. Either player can identify a top choice (or choices in the case of indifference) for any

subset of size 2. This is always the case as long a person’s preferences satisfy comparability.

There are 5 subsets with 3 or more outcomes: wxy, wxz, wyz, xyz and wxyz. Mr. i’s and Ms. j’s

most-preferred outcomes over these subsets are shown in Table l. Where either actor cannot state

a most-preferred choice or choices, the table contains a ‘-’.

Mr. i Ms. j
Subset Top choice Cycle? Top choice Cycle?
wxy x No x,y No
wxz - Yes x No
wyz w No y No
xyz - Yes x,y No
wxyz - Yes x,y No
Table l: Mr. i’s and Ms. j’s preferences for within subsets of the outcomes.

Preference orderings over a subset of outcomes which contain a strict preference cycle through

all of the elements in the subset have no articulable top choice. Preferences orderings over a

subset of outcomes which contain a strict preference cycle through less than all of the outcomes

in the subset may or may not have an articulable top choice. By way of comparison, note that i

has no top choice among the subset wxyz, but an individual with the following preferences



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would strictly prefer w despite the presence of a cycle through x, y and z: wPx, wPy, wPz, xPy,

yPz, and zPx.

Thus, transitive preferences are a sufficient condition for identifying top choices with respect to

any possible set of outcomes. Technically, acyclic preferences over all triples of alternatives in a

subset are necessary and sufficient for each subset to possess a maximal element. Acyclicity is

defined, for any x, y, z, as: if xPy, yPz then not zPx. Transitivity implies acyclicity and thus is

sufficient for the existence of a maximal element. Inasmuch as maximizing behavior often relies

on specifying clear ordinal rankings among outcomes, transitive preferences are effectively a

prerequisite for a rational choice approach to individual decision-making.

5. A reasonable assumption is that Senator Clinton’s preferences at that point were as

follows: P > S > C. Because she chose the office of Secretary of State, it would not be reasonable

to assume that P > C > S. The assumption that P > S is stronger, but corresponds with reports in

the media at the time.



The fact that Senator Clinton chose the position within the administration implies the following:

S > (l — p)C + p(P ). The chance to serve as Secretary of State was preferred to a risky ‘lottery’

over remaining in the Senate and eventually becoming President. We can rearrange the parts of

the inequality to derive



the following statement: S—C



> p. Thus, the lowest p which would induce Hillary Clinton to stay in the




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Senate is S—C



= p, and any p greater than S—C



would induce a strict preference for remaining in the



Senate. This relation also suggests three interesting comparative statics when all other variables

are held constant: l. there is a threshold as S increases at which one cannot resist the offer of the

Secretaryship; 2. there is a threshold as P increases at which one will reject the Secretaryship and

hold out for a chance at the Presidency; and, 3. as C increases the threshold p at which one will

accept the Secretaryship decreases. This latter effect occurs because as serving in Congress

becomes more desirable, the lottery over C and P becomes more appealing relative to the S.



6. Recall that the theory of expected utility states that given two different lotteries, L and L′,

over the same outcomes, then LPL′ if and only if ΣxєX p(x)u(x) > ΣxєX p′(x)u(x). Using this

definition we can get the

following two relations about Ll and L2, and L3 and L4:




The trick here is to manipulate these expressions to show that they imply a contradiction.

Consider the following two steps: add .89u(z) to both sides of the first expression, and then

subtract .89u(y) from both sides of the first expression. This yields:



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which contradicts our second expression.

Two steps in this process require further justification. First, is it okay to add and subtract

constants to an expected utility expression? This is fine: expected utilities act like numbers and

adding the same number to each side of an expression will not change the overall preference

relation. If I prefer 2 apples to l orange, then I should also prefer 2 apples and lO units of utility

to l orange and lO units of utility. Second, can we take these ‘manipulated’ expressions and treat

them as identical to a genuine lottery? If we are smart about our manipulations (i.e. add and

subtract things so that we still have a proper probability distribution where all of the probabilities

are between O and l, and also sum to l) then we can treat the new objects as ordinary lotteries.

This is what allows us to compare our manipulated version of expression l with expression 2.




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