UNIT 3: POLITICAL PARTIES/INTEREST GROUPS/MEDIA/ELECTIONS

VOTING METHODS

• What type of voting method do we use in the US? What’s the problem? – Since 1828, at least 5 elections have been decided by

spoilers (1912-Taft, Roosevelt, Wilson)

• Other systems: – Approval-

– Borda

– Condorcet

– Instant Runoff

– Range

VOTING METHODS

VOTING METHODS

APPROVAL

Candidate with the most votes wins EX: Mathematical Association of America, Papal enclaves from 1200-

1600s, Republic of Venice

VOTING METHODS

Candidate with the lowest points wins EX: Slovenia, Heisman Trophy, MVP of Major League Baseball

BORDA

1 POINT

2 POINTS

3 POINTS

4 POINTS

VOTING METHODS

CONDORCET

If there is a candidate who would defeat all others in a one on one matchup, that candidate wins. (Rock-Paper-Scissors Problem)

EX: rare, mostly private organizations

VOTING METHODS

INSTANT RUNOFF

Each ballot is assigned to its highest ranked candidate. If one candidate wins more than half the ballots, that candidate wins.

Otherwise the candidate with the least 1st place votes is eliminated and those ballots are redistributed to the next highest non-

eliminated candidate.

EX: Australia, India, San Francisco, Minneapolis, Aspen, Memphis

INSTANT RUNOFF

VOTING METHODS

RANGE

Candidate with the highest average wins.

EX: pretty much everything on the internet (Amazon, IMDB); bees in nature

VOTING METHODS

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Proof of Arrow’s Impossibility Theorem

From: J. Kelly, Social Choice Theory: An Introduction

If you are interested in more detail on axiomatic social choice theory,

Kelly’s book is the best place to start.

I. Arrow's General Impossibility Theorem

A. The Axioms: Properties we would want a social choice function to have

1. Collective Rationality: the social preference relation is reflexive, transitive and

complete.

a. Kelly (1988) says that a choice function is explicable if there is a

relation, S, such that

C(v) = {x 0 v: x S y, œ y 0 v}

b. Furthermore, a choice function has a transitive explanation if S is

reflexive, complete, and transitive.

c. Then we say that a social choice rule (or function) has transitive

explanations if at every admissible profile, R, the associated CR has a

transitive explanation.

d. Essentially, this says that we want our social choice function to have the

same minimal property of rationality that individuals have.

(1) Specifically, it says we don't want any cycles of the sort that

Condorcet identified.

(2) Note the implication: collective rationality rules out the

Condorcet producedure.

2. Unrestricted Domain: the social preference function has as its domain all

logically possible profiles of preference orderings on O and all possible agendas v

d O.

a. This says that, at least a priori, we have no reason in a democratic

political system to define any particular individual preference ordering, and

thus we cannot rule out any particular profile.

b. Note that this may be violated by real societies where, say, socialization

makes certain profiles very unlikely.

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3. The Pareto Property

a. Variants of the Pareto Property

(1) Weak Pareto Principle: For x and y 0 O, if x Pi y œ i 0 I, then

x PS y.

(2) Strong Pareto Principle: Let the social choice rule select

choice function CR at profile R. Suppose that at R everyone

unanimously finds one alternative, x, to be at least as good as y (x Ri

y œ i 0 I), and at least one individual strictly prefers x to y (x Pi y

for at least one person). Then, if x is available (x 0 v), y won't be

chosen (y ó CR(v)).

(a) The strong Pareto principle is “strong” in the sense that

it excludes more alternatives from the chosen set than the

weak pareto principle.

b. These insist on a very weak form of democratic-ness. Specifically, these

are attempts to implement formally the notion that democratic social choice

rules should be positively responsive to preferences.

c. The Pareto principle captures notions like

(1) Monotonicity: if some individual raises her evaluation of a

chosen alternative (all other evaluations held constant), that

alternative cannot cease to be chosen; or, if some individual lowers

her evaluation of a non-chosen alternative (ceteris paribus) that

alternative cannot become chosen.

(2) Non-Imposition

4. Independence of Irrelevant Alternatives (IIA): If R is a profile over some set

of alternatives that includes x and y, if G(R, {x,y}) = x PS y (i.e. CR({x,y}) = x),

and if RN is another preference profile such that each individual's preferences

between x and y are unchanged from the first profile, then G(RN, {x,y}) = x PS y.

a. Example of failure of independence for the Borda rule

(1) Consider the 3 person profile R

(a) xyzw

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(b) yzwx

(c) zwxy

(d) With 4 alternatives, we assign 4 points for a first-place

ranking, 3 for a second, 2 for a third, and 1 for fourth.

Thus, the Borda scores for this profile are:

i) w = 6

ii) x = 7

iii) y = 8

iv) z = 9

(2) Here is another 3 person profile, RN

(a) xzyw

(b) ywxz

(c) wxzy

(d) The Borda scores here are

i) w = 8

ii) x = 9

iii) y = 7

iv) z = 6

(3) Now consider the agenda v = {x,y,w}, i.e. delete z.

(a) G(R. v) = y, and G(RN, v) = x.

(b) This is problematic since we are getting different choices

from v even though the two profiles agree completely over

this agenda.

b. The assumption of independence says that this is an unattractive

property for a social choice rule so, if two profiles R and RN, restricted to

an agenda v are identical, then the choices made from that agenda should

be the same.

c. Let me just warn against a common misunderstanding of this condition:

independence does not rule out "intensity" of preference in making social

choices.

(1) It is part of our definition of a social choice rule/function that

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the choices are based only on the information in a profile of ordinal

preference relations.

(2) These preference relations do not contain any intensity

information that could be used by social choice rules, whether or

not they violate the independence axiom.

d. Note the difference between transitivity and independence

(1) to check whether there is a transitive explanation you fix the

profile and vary the agenda; while

(2) to check independence you fix the agenda and vary the profile.

5. Nondictatorship: No person i is decisive for every pair of outcomes in O.

a. Decisiveness: A group g, or individual i, is said to be decisive for

alternate x against alternate y if at every profile in the domain of the rule, if

x Pi y for individual i, then for any agenda containing x, y will not be

chosen--even if all non-g's prefer y to x.

b. If individual i is decisive for every pair of alternatives in O, we say that

the individual is a dictator.

B. Theorem (Arrow, 1950, JPE): If O consists of 3 or more outcomes, the only rules that

satisfy collective rationality, unrestricted domain, the pareto principle, and independence

of irrelevant alternatives, violate nondictatorship.

1. Think about what this says: it doesn't say that it is difficult to find a social choice

rule that satisfies these five axioms, it says it's impossible.

2. This is all the more striking because this is a fairly short list of axioms. Real

world social choice rules have many more properties than these.

a. e.g. we might want the rule to select a unique alternative; or we might

want to grant individuals decisive power over certain classes of decision

(e.g. we might want to let people decline elective office).

b. In fact, Arrow set out to prove that such functions do exist.

3. Furthermore, all of the axioms attempt to get at things that we would generally

take to be desirable properties of social choice rules.

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C. Proof:

1. The strategy of the proof is to assume that all five conditions hold and derive a

contradiction.

a. This will prove that the assumption that the five conditions hold is false.

b. Following Kelly (1988) we will develop three preliminary results called

contagion theorems.

c. A little jargon and notation:

(1) Suppose that there are N individuals, a subset T d N is locally

decisive for alternative x against alternative y if, whenever profile R

satisfies

(a) x Ri y, œ i 0 T;

(b) x Pi y, for at least one i 0 T; and

(c) y Pj x, œ j 0 N - T;

then x 0 v implies y ó CR(v). Note that this is only exclusionary

power, not the power to select.

(2) If T is locally decisive for x against y, T can exclude y (if x is

available and members of T prefer x to y) but this exclusion only

takes effect if everyone ouside T strongly prefers y to x.

(3) A set is called decisive (or globally decisive) for x against y if it

can exclude y no matter what pattern of preferences on x and y are

held by people not in T.

(4) If a set T is locally decisive for x against y we will write x DT y;

if T is globally decisive against y we will write x DT* y.

2. Lemma 1 (First Narrow Contagion Result): Suppose with at least three

individuals and at least three alternatives, a social choice rule satisfies collective

rationality, unrestricted domain, strong Pareto condition, and IIA. If for this rule

T is locally decisive for a against b, then T is globally decisive for a against c,

where a, b, and c are distinct alternatives in O.

Proof: Assume a DT b and we seek to prove that a DT* c.

a. To prove a DT* c, we must show a 0 v implies c ó v at any profile R

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where everyone in T finds a to be at least as good as c and one strictly

prefers a.

b. So let R be such a profile and partition T into T1 and T2, such that

everyone in T1 has a Pi c and everyone in T2 has a Ii b. The remaining

individuals in N, N-T, may have any orderings of a and c (in particular,

they may have the same or different orderings). In Kelly's notation this is

(1) T1: ac

(2) T2: (ac)

(3) N-T: [ac]

c. Now we want to show that a 0 v implies c ó CR(v). Since CR has some

transitive explanation by S, it is equivalent to show a S c and not c S a.

(1) It can be shown that if unrestricted domain holds, there is a

unique S that explains CR, namely

x S y iff x 0 CR({x,y}).

(2) Thus, it is sufficient to prove CR({a,c)} = {a}.

(3) To prove this, we consider a new profile, constructed to be very

closely related to R.

(a) Profile RN, restricted to {a,b,c} is

(b) T1: abc

(c) T2: (abc)

(d) N-T: b[ac]

(e) In this case the square brackets imply that, whatever

ranking an individual in N-T had of a and c at R, it is

unchanged at RN by the addition of b, which dominates

both.

(4) By unrestricted domain, the social choiice rule yields a choice

function CR'.

(5) Another application of the domain constraint tells us that {a,b},

{a,c} and {b,c} are in the domain of CRN.

(6) By local decisiveness of T for a against b (and noting that

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everyone in T finds a Ri b, someone in T1 finds a Pi b, and everyone

in N-T finds b Pi a) we get CRN({a,b}) = a.

(7) From the strong Pareto condition (and noting that at RN

everyone finds b to be at least as good as c--b Ri c œ i 0 I) we get

CRN({b,c}) = {b}.

d. From CRN({a,b}) = {a} and CRN({b,c}) = {b}, we now want to show that

CRN({a,c}) = {a}.

(1) First, we exploit our knowledge that CRN has some reflexive,

complete and transitive explanation, SN:

(a) From CRN({a,b}) = {a} we get a SN b;

(b) From CRN({b,c}) = {b} we get b SN c;

(c) These, with transitivity of S' give a SN c.

(d) By reflexivity a SN a.

(2) Together with the fact that SN explains CRN, these tell us that

that a 0 CRN({a,c}).

(3) To complete the proof, we want to show that c ó CRN({a,c}).

(a) Suppose not. Then c SN a.

(b) Since also b SN c, transitivity gives b SN a.

(c) Together with b SN b, this would tell us that b0

CRN({a,b}), which is false.

(d) Thus c ó CRN({a,c}) and so CRN({a,c}) = {c}.

e. Finally, since R and RN agree on {a,c}, one application of IIA yields

CR({a,c}) = {a},

which is what we wanted to show€

3. Lemma 2 (Second Narrow Contagion Result): Suppose with at least three

individuals and at least three alternatives a social choice rule satisfies unrestricted

domain, strong Pareto condition, IIA, and has transitive explanations. If for this

rule a set T is locally decisive for a against b, then T is globally decisive for c

against b, where a, b, and c are distinct alternatives in O.

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Proof: Just like the first narrow contagion result.

4. Lemma 3 (Broad Contagion Result): Suppose with at least three individuals

and at least three alternatives a social choice rule satisfies unrestricted domain,

strong Pareto condition, IIA, and has transitive explanations. If for this rule a set

T is locally decisive for one alternative against another, then T is golbally decisive

between any two alternatives.

Proof: Suppose that x DT y; we wish to show that z DT* w, were z and w

are any two alternatives in O. The proof works in two parts--first show

that broad contagion holds over any triple of alternatives and then use this

to show that it holds over all of O.

5. Proof of Arrow's Theorem: Assume that all five conditions hold. Now we will

show that this implies a contradiction.

a. By the strong Pareto condition, there exist decisive sets.

(1) Let T be a decisive set of the smallest size (if there are more

than one, just pick one arbitrarily).

(2) By the no dictator condition, T must have at least two members.

(3) From T choose one member, who will be called k.

(4) T - k is still non-empty.

(5) Consider the following profile (which should be familiar from

the Condorcet paradox), R:

(a) k: xyz

(b) T-k: yzx

(c) N-T: zxy

b. The contradiction we are after takes the form of showing that k must be

a dictator.

(1) By the broad contagion result, it is sufficient to show that k is

locally decisive for x against z.

(2) By IIA is would suffice to show that, at R, CR({x,z}) = {x} for

then x alone would be chosen from {x,z} at any profile that, like R,

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has k strictly preferring x to z and everyone else opposed.

c. Since T is decisive, CR({y,z}) = {y}.

(1) If CR({x,y}) = {y}, then IIA would tell us that T-k is locally

decisive for y against z.

(2) But then the broad contagion result says that T-k is decisive,

contrary to our choice of T as a minimal decisive set.

(3) Hence CR({x,y}) … {y} , i.e. x 0 CR({x,y}).

d. Now recall that CR is explainable by a reflexive, complete, transitive S.

(1) From x 0 CR({x,y}), we get x S y;

(2) From y 0 CR({y,z}) we get y S z; and

(3) From transitivity we get x S z, thus x 0 CR'({x,z}).

e. Now we only need to show that z ó CR({x,z}).

(1) Suppose that it is. Then z S x which, with x S y, tells us that z

S y, which we know is false from CR({y,z}) = {y}.

(2) Thus, CR({x,z}) = {x}, which implies that k is a dictator.

f. This is a contradiction, which implies that no social choice function can

satisfy all five conditions €

ARROW’S IMPOSSIBILITY THEOREM

Some Election Key Terms

– Closed primaries: Only people who have registered with the party can vote for that party’s candidates.

– Open primaries: Voters decide on Election Day whether they want to vote in the Democrat or Republican primary.

– Blanket primaries: Voters are presented with a list of candidates from all parties. (declared unconstitutional on more than one occasion Washington/Alaska/California)

VOTING METHODS

• When voting goes wrong…..the 1991 Louisiana gubernatorial election: a case study

• Louisiana’s “jungle primary”= all candidates from all parties run in the same primary. Top two move on to a runoff.

Candidate Affiliation Support Outcome

Edwin Edwards Democratic 1,057,031 (61.2%) Elected

David Duke Republican 671,009 (38.8%) Defeated

Candidate Affiliation Support Outcome

Edwin Edwards Democratic 523,096 (33.8%) Runoff

David Duke Republican 491,342 (31.7%) Runoff

Buddy Roemer Republican 410,690 (26.5%) Defeated

Clyde Holloway Republican 82,683 (5.3%) Defeated

Sam Jones Democratic 11,847 (0.8%) Defeated

Ed Karst No Party 9,663 (0.6%) Defeated

Fred Dent Democratic 7,835 (0.5%) Defeated

Anne Thompson Republican 4,118 (0.3%) Defeated

Jim Crowley Democratic 4,000 (0.3%) Defeated

Albert Henderson Powell

Democratic 2,053 (0.1%) Defeated

Ronnie Glynn Johnson

Democratic 1,372 (0.1%) Defeated

Ken "Cousin Ken" Lewis

Democratic 1,006 (0.1%) Defeated

1st BALLOT

VOTING METHODS

• “vote for the lizard, not the wizard”

• “vote for the crook, it’s important”

VOTING METHODS

• Proportional representation- number of seats is proportional to number of votes received (Ex: a party gets 10% of votes then they get 10% of seats)

• Our electoral college uses a plurality system except for two states

Political Parties

• What is a political party?

• Why are American political parties unique?

Political Parties

• History of American political parties:

– Founding to 1820s

– Jacksonians

– Civil War and sectionalism

– Era of Reform

– New Deal Era

– Modern era

Political Parties – Three Key Terms

• Delalignment

Abandonment of citizens from identifying with the two political parties.

• Critical election

An electoral “earthquake” in which the election results produce surprising change.

• Realignment

Change in the political party that occurs after a “critical election”. Change includes platform, demographic support, & change in majority. Change is national as well as local and has permanence.

Dealignment

A look at proportional elected legislatures vs. single member

district legislatures Proportional election 100 seats

10% party A = 10 seats

40% party B = 40 seats

50% party C = 50 seats

In a Single Member District system with the same nation wide percentages is likely to yield

Party B wins 45 seats Party A wins 0 seats

Party C wins 55 seats

Party Realignments

• Why are these a big deal?

1.1796 Federalists and Anti Federalists

2.1828 Jacksonian Democrats vs. Whigs

3.1860 Two Republican Eras

4.1932 The New Deal Coalition

Today – the era of “Divided Government”

Was the election of 1994 a realignment?

(1) President Clinton began his presidency with a Democratic controlled Congress. Democrats had controlled Congress for 40 years.

Was the election of 1994 a realignment?

(2) In 1994 the mid-term election Republicans took control of Congress, with Newt Gingrich as the Republican Speaker of the House, promising to implement a “Contract with America” or a series of conservative policies.

The two party system

Political Parties

– Conventions-

• superdelegates

– Hatch Act of 1939: prevented federal civil service employees from taking active partisan roles in parties, elections, etc. They can vote and contribute funds, but active campaigning, running for office, solicitation of funds, etc. is forbidden.

– Why the 2 party system?

Political Parties

– Minor parties

• Why so little success?

Political Parties

• Presidential nomination process

• Presidential vs congressional campaigns

• Running for president or……(how to become POTUS)

– Primary vs general campaigns

– Media effects

Campaign Finance

• Presidential Primaries – part private, part public funds (public matching funds can be waived to avoid spending limits). Private funds include individual ($2,000 maximum per election) and PAC ($5,000 maximum per election) donations. Public matching funds (dollar for dollar) are available only for candidates who raise at least $5,000 in at least 20 states in small contributions ($250 or less each).

• Presidential General Elections – historically, the federal government has picked up the entire tab, but George W. Bush (2000 and 2004) and John Kerry both turned down this federal money and used only private funds to avoid spending limits (Congress would have appropriated about $70 million in 2004 to each candidate).

• Third parties – only receive federal presidential campaign funds if they receive 5% or more of the vote nationally. Higher percentages receive higher funding.

• Congressional Elections – no public funding – all private (individuals, PAC’s, and parties). Campaign finance limits apply.

• Conventions – Congress pays for the parties nominating conventions.

Campaign Finance

• FECA- 1974- sets limits, requires disclosure of contributions and spending, institutes public financing; leads to……PACS

• Buckley v. Valeo- strikes down portion of FECA which restricts money a person can spend on his own campaign; money=speech; TV ads are regulated BUT……not if they don’t “advocate” a candidate…..what do we get……..ATTACK ADS

• Soft money use explodes– unregulated donations to political parties, not specific candidates; 1996 Clinton campaign;

• 527s – tax exempt organizations which are unregulated because they do not coordinate activities with a party or candidate

• Bipartisan Campaign Reform Act (McCain-Feingold) – shuts down soft money and “sham issue ads” within 60 days of a general election

• Citizens United v. US (2010)- corporations allowed to expressly advocate for a candidate

Campaign Finance

• Effects of finance reform

• Advantages of incumbency

• Prospective vs Retrospective voting

Interest Groups

• An interest group is an organization of people whose members share policy views on specific issues and attempt to influence public policy to their benefit.

• Why so common in America?

• Institutional vs Membership interests

• Interest group activities

• PAC money

• Specific examples: AARP NAACP Sierra Club AFL-CIO NRA

Interest Groups

Interest Groups

• Differences between political parties and interest groups

• Types of interest groups

• Fundamental goals of interest groups

• Lobbying

• Influence theories – Power Elite theory

– Pluralist theory

– Hyperpluralist theory

MASS MEDIA

• Historical progression of American journalism

• What does the “national media” consist of?

• 3 Primary roles of the media in politics

• TV regulations

• New social media

• Are news stories biased?

• Government constraints on media

MISCELLANEOUS

• Caucuses • Superdelegates • Electioneering • free-rider problem • Linkage • Referendum • Initiative • Recall • Why no internet voting?

Terms Most Likely To Be On the AP Exam

• Political party • Plurality election • Single-member district • Party era • Critical election • Party realignment • Divided government • Interest group • PAC • Free riders • Power-elite theory • Pluralist theory • Hyperpluralist theory • Mass media • Linkage institutions • Horse-race journalism • Closed primary • frontloading