Three Cheers for the Blue, Red, and Purple

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Three Cheers for the Blue, Red, and Purple

• Domestic Migration and Polarization in U.S.
  Politics
• EITM V, University of Michigan
• Ian McDonald, Duke University
• ian.mcdonald_at_duke.edu

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Agenda

• Motivation
• Sorting What is it? Why should it matter?
• Hypothesis
• Key Assumptions
• Baseline Model and Utility Function
• Expected Results
• Problems and Next Steps

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Motivation

• Does migration in America sort voters?
• Do voters with similar political preferences
  gravitate to the same places?
• Process may be neither self-conscious nor overtly
  political.
• If so, when and where?
• Does sorting contribute to institutional
  polarization, in Congress and elsewhere?

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Motivation

• What Does Sorting Look Like?
• US Presidential Elections of 1976 and 2000
• Two extremely close elections
• Counties where candidate gets gt 60 of two-party
  vote
• 1976 27 2000 45
• So, is the electorate more geographically
  polarized?
• If so, is this a result of migration?
• Three Possible Answers
• Yes, No, and It Depends Where You Look

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Hypothesis

• Some potential hypotheses
• () Wealthy migrants sort themselves more
• Corollary Wealthier places are more extensively
  sorted.
• Corollary Overall sorting increases as overall
  wealth increases.
• () New arrivals in a large scale migration to a
  sparsely populated place sort themselves more.
• New settlement creates an opportunity for
  sorting.
• Not necessarily associated with wealth.
• ( or -) Sorting could increase or decrease
  because of
• Demand for public goods (education, specifically)
• Different migration costs for various age groups.

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Proposed Model

• This model focuses on the wealth hypothesis
• Does greater individual wealth and overall
  prosperity lead to sorting of political
  preferences?

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Hypothesis

• Definition
• Affinity is the extent of shared preferences
  among residents in a single location, of any
  granularity

These triplets have affinity!
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Hypothesis

• Proposed Axiom
• Affinity is valued and scarce
• Many people want it, for its own sake
• It can result from processes that attract wealth,
  and thus
• People in wealthy places tend to have similar
  preferences

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Proposed Model

• I Propose an Agent Based Computational Model
• Well suited to migration models because
• Dynamic and reveals changing equilibria
• Migration is adaptive movers dont search the
  entire space for optima
• Models can reflect the spatial organization of
  the actual residential landscape
• Model can evolve to reflect persuasive influence
  of other agents

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Proposed Model

• Space is organized into generic districts
• Each cell is a single district, and each district
  can support any number of agents
• Each district has a wealth threshold. Agents who
  dont meet the threshold cant live there
• Agents have two exogenous attributes
• Wealth A one time endowment at startup
• Preference A one-dimensional preference
  profile i.e., one number
• The model is based on an agent utility function.
• Agents seek districts that maximize
• wealth threshold of their district, as described
  above, and
• affinity, community proximity to agents
  preferences

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Proposed Model

• Utility Function
• Ui f(wealth thresholddistrict, affinityi),
• Individual endowment must exceed threshold
• Ui ß1wealth thresholddistrct ß2affinityi
• Where ? ßi 1
• District Wealth and Agent Wealth
• Each based on initial endowment
• Affinity - Preference - District Mean
  Preference 2
• Beta Coefficients are global
• Agents then search the vicinity for higher utility

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Proposed Model

• In a Nutshell
• Agents have some wealth, a preference profile,
  and an affinity level with neighbors
• Districts have a wealth requirement (aka
  threshold)
• Agents want to live in wealthy districts and have
  affinity with their neighbors
• Based on some exogenous weighting
• As agents move around, the utility of agents left
  behind can change,
• And so it goes.

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Richer districts should be more homogenous
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Key Assumptions

• Wealth and preference are independent and do not
  co-vary (emphasis added)
• All individual preferences (i.e., all beliefs,
  all tastes) are fixed, exogenous, and one
  dimensional.
• Each agent has a single consolidated preference
  value.
• For example
• The left anchor could be Che Guevara who shops at
  REI
• The right anchor could be Genghis Khan who shops
  at WalMart
• All possible preferences and tastes are collapsed
  on to one dimension
• Preference is exogenous affinity is endogenous
• Agents prefer wealthier districts, given constant
  affinity
• No external cultural influence on preferences

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Proposed Model

• Other Rules
• Each agent begins in a district with a wealth
  threshold equal to, or lower than, her own wealth
• Each cell contains any number of agents

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Expected Results

• If the hypothesis is correct, moves should
• Increase overall utility and
• Increase overall affinity shrink preference
  dispersion
• Approaching equilibrium
• Utility changes, and may shrink, if preferred
  neighbors move away and disliked neighbors move
  in.
• In equilibrium
• if Beta 1 is high and Beta 2 is low
• Overall utility goes up a lot, and affinity goes
  up a little
• If Beta 1 is low and Beta 2 is high
• Overall utility goes up a little or drops, and
  affinity goes up a lot for wealthy districts.

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Problems and Next Steps

• Larding the Model Potential additions
• Apply agent-specific beta coefficients
• e.g., Different combinations of beta might apply
  to different age ranges
• Explore the Empty Space Hypothesis
• Add each agents value of a public good (I.e.,
  education) to the utility function.
• Presumably correlated to wealth
• Add cost component to moves
• Add exogenous wealth shocks
• Endogenize preferences (using neighbors and other
  agents)

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Problems and Next Steps

• Characterizing wealth
• Poor migrants could increase homogeneity
• Identifying and observing affinity
• Needs very careful, concrete definition
• Arguably, should be multi-dimensional
• Figure out Theoretical Basis for Weighting
• What are well grounded coefficients?
• Easier to justify ordinal weightings vs. cardinal
• Ensure the outcome isnt pre-ordained or
  tautological
• Ask for your help, and thank Rob and Carolina