Introduction to Rational Choice

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Introduction to Rational Choice Game Theory I

• Syllabus http//www.politics.ubc.ca/index.php?id
  6302
• Required Texts

2
Introduction to Rational Choice Game Theory I

• Rational Choice Theory
• Way of thinking about politics
• Positive rather than normative, i.e., what is
  rather than what ought to be
• Methodological individualism
• Deductive moves from assumptions to inference

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Introduction to Rational Choice Game Theory I

• Defining Rationality
• Rationality as Self-Interest
• What do we mean by self-interested?
• NOT everyday selfishness
• NOT just narrow self-interest
• Long-term / enlightened self-interest

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Introduction to Rational Choice Game Theory I

• Defining Rationality
• What makes an actor rational?
• Actors have preferences (wants, goals)
• Fixed in short-run
• Acting as if to maximize preferences efficiently
• Preference ordering / utility function
• Complete
• Transitive

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Introduction to Rational Choice Game Theory I

• Preferences
• e.g., My preferences for ice cream
• pistachio P vanilla P chocolate
• Complete
• I have some feeling about all flavours
• Transitive
• I must prefer pistachio to chocolate given that I
  prefer a) pistachio to vanilla, and b) vanilla to
  chocolate

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Introduction to Rational Choice Game Theory I

• Preferences
• Ordinal
• I like pistachio more than vanilla, but I cant
  say I like it 3 times more just more
• No Inter-Personal Comparison
• I cant say my preference for pistachio exceeds
  your preference for vanilla
• Utility
• The satisfaction that I get from a payoff (i.e.,
  an outcome, like a pistachio ice cream cone).

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Introduction to Rational Choice Game Theory I

• Preferences
• Despite these limitations, we can do quite a lot
  with just information on actors preferences
• Consider Rikers story about trading votes at the
  US Constitutional Convention

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Two main issues
• Navigation Acts Bar British ships from US ports
• Should Congress pass by
• Simple (50) Majority?
• 2/3 Majority?
• Boon to New England shipping, but higher
  transportation costs to Southern exports
• For NE (50)P2/3
• For South 2/3P(50)

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Slave Trade key to Southern States
• Should slavery be prohibited
• Immediately
• At some point in the future (e.g., 1800)
• Critical to Southern ratification
• Offensive to Northern abolitionists
• South Future P Immediate
• North Immediate P Future

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Two issues generate four combination of positions
• Southern and Northern ideal combinations are
  readily visible
• But neither Southern nor Northern coalitions vote
  for their ideal packages?

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Both South and North try to get their best
  deals...
• The 3/5 Dilemma
• On what basis should House seats be apportioned?
• South wanted to offset the Norths population
  advantage by counting slaves in their population
  totals

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The 3/5 Dilemma
• North cannot accept this position
• Gouvenor Morris sees logical, moral strategic
  problems
• Are they slaves men? Then make them citizens
  and let them vote? Are they property? Why then
  is no other property included?
• What is the proposed compensation to the
  Northern States for a sacrifice of every
  principle of right, of every impulse of
  humanity?
• On the other side the Southern States are not to
  be restrained for importing nay they are to be
  encouraged to it by an assurance of having their
  votes in the Natl. Govt. increased in proportion

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Report of Committee on Detail Article VII (Sec 4
  6)
• Section 4.1 No tax or duty by Congress on state
  exports
• Clause 2 Nor on migration or importation of
  persons
• Clause 3 nor shall migration or importation be
  prohibited
• Section 6 No navigation act shall be passed
  without assent of 2/3 of members present in each
  House

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The Southern Response
• The Southern States could not be members of the
  Union if the clause i.e., Art VII, Sec 4, cl.
  2-3 should be rejected. Williamson (NC)
• Morris increases the pressure
• delete persons in Sec. 4.2, and substitute
  slaves into North Carolina, South Carolina, and
  Georgia.
• The Southern counter
• ...if himself and all his colleagues were to
  sign the Constitution and use their personal
  influence, it would be of no avail toward
  obtaining the assent of their Constituents.
  Charles Pickney (SC)

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The bargaining helps to reveal preference
  orderings
• South continued slavery P failure of Convention
  P ratification immediate stop to slavery
• What should happen if the North insists on an
  immediate stop to the slave trade?
• Staunch federalists like Morris Madison dont
  want the Convention to fail
• Ratification (of some sort) P immediate ban on
  slavery

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The Strategic Situation

Refuse
Insist on Immediate Prohibition
S
Accept
N
Accept Delayed Prohibition
Refuse
S
Accept
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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The Strategic Situation

Refuse
Insist on Immediate Prohibition
S
Not a sensible outcome for the South
Accept
NE
Accept Delayed Prohibition
Refuse
S
Accept
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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• A Vote Trade
• With ratification on the line, Morris proposed
• the whole subject to be committed including
  clauses relating to the tax on exports and to a
  navigation act. These things may form a bargain
  among the Northern and Southern States.

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8
A log-roll North and South get their 2nd
Preferences, giving up the part of the
combination they value less
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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• Two issues generate four combination of positions
• Southern and Northern ideal combinations are
  readily visible
• But neither Southern nor Northern coalitions vote
  for their ideal packages?

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Trading Votes at the Constitutional Convention
Riker, Art of Political Manipulation Ch. 8

• The Strategic Situation

Agree to 50
3, 0
Insist on Immediate Prohibition
S
1, 1
Insist on 2/3
NE
Agree to 50
Accept Delayed Prohibition
S
2, 2
Insist on 2/3
0, 3
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Under the Confederation Windows Moore, Ch. 4
Moore tells a similar story...
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Under the Confederation Windows Moore, Ch. 4

• The Quebec Conference
• The best interests and present and future
  prosperity of British North America will be
  promoted by a Federal Union under the Crown of
  Great Britain, provided such Union can be
  effected on principles just to the several
  Provinces.
• "Report of Resolutions Adopted at a Conference
  of Delegates From The Provinces of Canada, Nova
  Scotia And New Brunswick, And The Colonies of
  Newfoundland And Prince Edward Island, Held at
  The City of Quebec, 10th October, 1864, as The
  Basis of a Proposed Confederation of Those
  Provinces And Colonies." Journal of the House of
  Assembly, 1865, Appendix, pp 854-73.

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Under the Confederation Windows Moore, Ch. 4

• What were just principles?
• Brown Upper Canada Reformers rep-by-pop
• Cartier the French-Canadians sectional
  equality
• Maritime Provinces local autonomy
• Federalism by default
• Written constitution...
• What governmental structure?

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• 6. There shall be a General Legislature or
  Parliament for the Federated Provinces, composed
  of a Legislative Council Senate and a House of
  Commons.
• How should Senate be structured and selected?

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• The Canadian position
• Sectional equality of regions
• Ontario Quebec Maritimes
• John A. This is a concession to Maritimers.

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• The Maritime Response (A. MacDonald, PEI)
• If rep-by-pop prevails in Commons, the upper
  house should be more representative of smaller
  provinces, as it was to be the guardian of their
  rights and privileges (105)
• An American-style Senate

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• An American-style Senate
• US Civil War fuels suspicion
• Threats to quit on both sides
• Tuppers compromise
• Extra seats for region if / when Newfoundland
  joined

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• The method of selection Appointment or Election
• Appointment by federal government unanimously
  approved
• just the worst body that could be contrived
  ridiculously the worst. (Christopher Dunkin in
  Moore, 107)

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Under the Confederation Windows Moore, Ch. 4

• The Senate (Legislative Council)
• Were Fathers just myopic, foolish, or
  anti-democratic?
• Why did Martimers so readily bargain away
  provincial equality in Senate?

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Under the Confederation Windows Moore, Ch. 4

• A Strategic Bargain?
• Reformers worry about an elected Senate
• A legitimate conservative check
• Threat to responsible government
• The question, I think, fairly presents itself
  whether two elective chambers , both representing
  the people and both claiming to have control over
  the public finances would act together with the
  harmony necessary to the right working of
  parliamentary government.
• (Brown in Moore, 111)

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Under the Confederation Windows Moore, Ch. 4

• A Strategic Bargain?
• Reformers worry about an elected Senate
• A legitimate conservative check
• Threat to responsible government
• And there is still another objection to
  elective councillors. The expense of election
  is so great as to banish from the house all who
  are not able to pay very large sums of money for
  the possession of a seat.
• (Brown in Moore, 111)

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Under the Confederation Windows Moore, Ch. 4

• A Strategic Bargain?
• Reformers preferences
• No Senate
• Weak appointed Senate
• Effective, elected, sectional Senate

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Under the Confederation Windows Moore, Ch. 4

• A Strategic Bargain?
• For the Maritimers, better a weak Senate
• to give no illusion of protecting provincial
  rights
• to prevent Canadian bargainers from claiming that
  they had done Maritimers a favour regarding the
  Senates structure
• Maritime preferences?
• American-style Senate
• Weak appointed Senate
• Effective, elected, sectional Senate

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Under the Confederation Windows Moore, Ch. 4

• A Strategic Bargain?
• Both Reformers and Martimers can get their second
  preference (and prevent their worst outcome) by
  voting for a weak Senate
• A log-roll generates an inefficient institution

36
Introduction to Rational Choice Game Theory I

• Utility Expected Utility
• Preferences are ordinal (hence lumpy)
• Utility is continuous interval
• How can we translate between lumpy preferences
  and continuous utility?
• We need a mapping from my preference to the
  utility that I get from having that preference
  satisfied

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Introduction to Rational Choice Game Theory I

• A Utility Function a mapping from preference to
  utility U is the function, U(x) is the value of
  U evaluated at x xPiy ? ui(x) gt ui(y) (In
  words x is (strictly) preferred by i to y if and
  only if the utility i gets from x is greater than
  the utility i gets from y.

Utility
Illogical one to many
Ui(x)
Logical many (or one) to one
x (e.g., the amount of ice cream consumed)
X1
X2
X3
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Introduction to Rational Choice Game Theory I
Just a little taste mmm... increasing marginal
utility
Ui(x), i.e., my utility from the ice cream
? U/?x gt 0
Amount of Ice Cream Eaten
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Introduction to Rational Choice Game Theory I
Exactly enough... I maximized my utility
Ui(x), i.e., my utility from the ice cream
? U/?x 0
Amount of Ice Cream Eaten
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Introduction to Rational Choice Game Theory I
Too much I overdid it... declining marginal
utility
Ui(x), i.e., my utility from the ice cream
? U/?x lt 0
Amount of Ice Cream Eaten
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Introduction to Rational Choice Game Theory I

• Utility Expected Utility
• Use lotteries to map from preferences to utility
• Do I prefer vanilla (2nd preference) for certain
  to lottery of 50 chance of pistachio (1st
  preference) and 50 chance chocolate ( 3rd
  preference)?
• By altering probability of getting 1st or 3rd,
  you can see how I trade-off middling versus best
  or worst payoffs
• Key Idea I am indifferent when my certain
  utility from my 2nd preference my expected
  utility from the lottery over my 1st or 3rd,
  preferences

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Introduction to Rational Choice Game Theory I

• Utility Expected Utility
• Political campaigns make arguments about
  contingent states of the world
• The Liberal-NDP-Bloc Coalition is a gang of
  socialists who will wreak economic havoc
• Government stability provides the best course of
  action
• The economy depends on the Coalition taking power
  and implementing its stimulus package
• We must stop Harpers dictatorship now (or
  else...)!

43
Introduction to Rational Choice Game Theory I

• Utility Expected Utility
• Consider each campaign as offering a lottery,
  e.g.
• Probability, p, that Coalition rescues economy
• Probability (1-p) that Coalition taxes us to
  death
• A voters expected utility of supporting the
  Coalition is therefore
• EUCoalition pRescue (1-p)Taxation

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Introduction to Rational Choice Game Theory I
Voters Utility
This line sets out the possible outcomes between
the two possible states of the world.
UER
UHT
Voters Income given
High Taxation
Economic Rescue
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Introduction to Rational Choice Game Theory I
Voters Utility
reducing to high taxation (of some value) if p
0
Voters Income given
High Taxation
Economic Rescue
46
Introduction to Rational Choice Game Theory I
Voters Utility
and to economic rescue (of some value) if p
1
Voters Income given
High Taxation
Economic Rescue
47
Introduction to Rational Choice Game Theory I
Voters Utility
and to the possibilities in between high taxes
and economic rescue as p varies from 1 to 0.
Voters Income given
High Taxation
Economic Rescue
48
Introduction to Rational Choice Game Theory I
Voters Utility
so that if p .5, the voters expected income
would fall exactly on the middle of this line...
Voters Income given
Expected Income if p .5
High Taxation
Economic Rescue
49
Introduction to Rational Choice Game Theory I
Voters Utility
but how much utility the voter gets from that
expected income is an open question
?
Voters Income given
Expected Income if p .5
High Taxation
Economic Rescue
50
Introduction to Rational Choice Game Theory I
Voters Utility
We ask the voter to compare lottery to a
certainty, e.g., the income in their current job
and the certainty that their wont be any raises
next year because of the crisis
UCJ
Voters Income given
Certain Income in current job
51
Introduction to Rational Choice Game Theory I
Voters Utility
We ask the voter to compare lottery to a
certainty, e.g., the income in their current job
and the certainty that their wont be any raises
next year because of the crisis
UCJ (only voter knows this utility for sure)
Voters Income given
Certain Income in current job
52
Introduction to Rational Choice Game Theory I
We ask the voter How do you feel about the
certain job versus a lottery of a) better
economic times that give you 1000 raise or
higher taxes that cost you 1000
Voters Utility
UER
UCJ
UHT
Voters Income given
Certain Income in current job
53
Introduction to Rational Choice Game Theory I
The voter might be indifferent between this
income and a 50-50 shot at the lower or higher
incomes
Voters Utility
UER
UCJ
UHT
Voters Income given
Certain Income in current job
54
Introduction to Rational Choice Game Theory I
In other words, UCJ .5ER .5HT So we know
that UCJ is exactly half way between UER UHT
Voters Utility
UER
UCJ
UHT
Voters Income given
Certain Income in current job
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Introduction to Rational Choice Game Theory I
In other words, UCJ .5ER .5HT So we know
that UCJ is exactly half way between UER UHT
Voters Utility
UER
UCJ
UHT
Voters Income given
Certain Income in current job
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Introduction to Rational Choice Game Theory I
A person who reacts this way is called
risk-neutral
Voters Utility
UER
UCJ
UHT
Voters Income given
Certain Income in current job
57
Introduction to Rational Choice Game Theory I
Voters Utility
But other voters might more utility from their
certain job than from the 50-50 lottery over
1000 raise or 1000 tax hike
UER
Certain Income
UCJ
ULottery
UHT
Voters Income given
Expected Income if p .5
High Taxation
Economic Rescue
58
Introduction to Rational Choice Game Theory I
Voters Utility
indeed, theyd always prefer less income at
higher probabilities so that their utility
functions would actually look like concave
curves these voters are risk averse
UER
UCJ
ULottery
UHT
Voters Income given
Expected Income if p .5
High Taxation
Economic Rescue
59
Introduction to Rational Choice Game Theory I
Voters Utility
Conversely, given a certain income, some people
would get as more utility from the lottery than
from the certain job Their utility functions
would actually look convex these voters are risk
acceptant
UER
ULottery
UCJ
Certain Income
UHT
Voters Income given
Expected Income if p .5
High Taxation
Economic Rescue
60
Introduction to Rational Choice Game Theory I

• We know that people tend to
• be risk-averse over gains
• be risk-acceptant over losses
• over-estimate subjective probability of rare
  events,
• and minimize regret rather than maximize utility