Split-Ticket Voting: An Implicit Incentive Approach Galina - - PowerPoint PPT Presentation

Introduction Model Efforts Rule Dynamics Empirics Summary

Split-Ticket Voting: An Implicit Incentive Approach

Galina Zudenkova

Department of Economics Universidad Carlos III de Madrid

North American Summer Meeting of the Econometric Society Boston University, June 2009

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation I

Current State of the Art

Split-ticket voting – citizens vote for candidates of different parties in simultaneous elections

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation I

Current State of the Art

Split-ticket voting – citizens vote for candidates of different parties in simultaneous elections Examples: presidential and congressional elections in US; elections of mayor for the city hall and of governor for the region in Spain

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation I

Current State of the Art

Split-ticket voting – citizens vote for candidates of different parties in simultaneous elections Examples: presidential and congressional elections in US; elections of mayor for the city hall and of governor for the region in Spain Literature on Split-Ticket Voting in the US elections:

Strategic Voting: Alesina and Rosenthal (1995, 1996); Chari, Jones and Marimon (1997)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation I

Current State of the Art

Split-ticket voting – citizens vote for candidates of different parties in simultaneous elections Examples: presidential and congressional elections in US; elections of mayor for the city hall and of governor for the region in Spain Literature on Split-Ticket Voting in the US elections:

Strategic Voting: Alesina and Rosenthal (1995, 1996); Chari, Jones and Marimon (1997) Empirical Evidence: Burden and Kimball (1998); Degan and Merlo (2007); Tam Cho and Gaines (2004)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation I

Current State of the Art

Split-ticket voting – citizens vote for candidates of different parties in simultaneous elections Examples: presidential and congressional elections in US; elections of mayor for the city hall and of governor for the region in Spain Literature on Split-Ticket Voting in the US elections:

Strategic Voting: Alesina and Rosenthal (1995, 1996); Chari, Jones and Marimon (1997) Empirical Evidence: Burden and Kimball (1998); Degan and Merlo (2007); Tam Cho and Gaines (2004)

To out knowledge, no literature on split-ticket voting in municipal and regional elections Here we study this problem

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city Split-ticket voting happened

• nce in 10 cities (Alcorc´
• n, Aranjuez, Arganda del Rey, Coslada,

M´

• stoles, Pinto, Las Rozas de Madrid, San Sebasti´

an de los Reyes, Torrej´

• n de Ardoz, Tres Cantos)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city Split-ticket voting happened

• nce in 10 cities (Alcorc´
• n, Aranjuez, Arganda del Rey, Coslada,

M´

• stoles, Pinto, Las Rozas de Madrid, San Sebasti´

an de los Reyes, Torrej´

• n de Ardoz, Tres Cantos)

twice in 3 cities (Collado Villalba, Legan´ es, San Fernando de Henares)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city Split-ticket voting happened

• nce in 10 cities (Alcorc´
• n, Aranjuez, Arganda del Rey, Coslada,

M´

• stoles, Pinto, Las Rozas de Madrid, San Sebasti´

an de los Reyes, Torrej´

• n de Ardoz, Tres Cantos)

twice in 3 cities (Collado Villalba, Legan´ es, San Fernando de Henares) three times in 1 city (Alcobendas)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city Split-ticket voting happened

• nce in 10 cities (Alcorc´
• n, Aranjuez, Arganda del Rey, Coslada,

M´

• stoles, Pinto, Las Rozas de Madrid, San Sebasti´

an de los Reyes, Torrej´

• n de Ardoz, Tres Cantos)

twice in 3 cities (Collado Villalba, Legan´ es, San Fernando de Henares) three times in 1 city (Alcobendas) four times in 1 city (Rivas-Vaciamadrid)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Motivation II

Why to study split-ticket voting in local simultaneous elections?

Evidence from Madrid Region. 2 parties: PP, PSOE

1991, 1995, 1999, 2003, 2007 simultaneous elections 24 cities with more than 40.000 inhabitants Split-ticket voting in a city = mayor and governor from different parties get majority in this city Split-ticket voting happened

• nce in 10 cities (Alcorc´
• n, Aranjuez, Arganda del Rey, Coslada,

M´

• stoles, Pinto, Las Rozas de Madrid, San Sebasti´

an de los Reyes, Torrej´

• n de Ardoz, Tres Cantos)

twice in 3 cities (Collado Villalba, Legan´ es, San Fernando de Henares) three times in 1 city (Alcobendas) four times in 1 city (Rivas-Vaciamadrid) never in 9 cities (Alcal´ a de Henares, Colmenar Viejo, Fuenlabrada, Getafe, Madrid, Majadahonda, Parla, Pozuelo de Alarc´

• n, Valdemoro)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap I

We apply implicit incentive approach in principal-agent framework to explain split-ticket voting in simultaneous elections for mayor and governor offices

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap I

We apply implicit incentive approach in principal-agent framework to explain split-ticket voting in simultaneous elections for mayor and governor offices Retrospective Voting: Principals (voters), in each period of an infinite horizon, reward agents (mayor and governor) with reelection based on their observed performance but through implicit reward rule

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap I

We apply implicit incentive approach in principal-agent framework to explain split-ticket voting in simultaneous elections for mayor and governor offices Retrospective Voting: Principals (voters), in each period of an infinite horizon, reward agents (mayor and governor) with reelection based on their observed performance but through implicit reward rule Voters can influence agents’ performance only through the choice of an evaluation rule

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap II We show:

1

If voters vote split-tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap II We show:

1

If voters vote split-tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period Otherwise, absolute performance evaluation rule is used in next period

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Roadmap II We show:

1

If voters vote split-tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period Otherwise, absolute performance evaluation rule is used in next period

2

Principals vote split-tickets less frequently than no split-tickets

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Motivation Roadmap Related Literature

Related Literature

Retrospective Voting: Barro (1973); Ferejohn (1986); Persson, Roland and Tabellini (1997); Banks and Sundaram (1993, 1996) Career Concerns: Holmstr¨

• m (1982); Dewatripont, Jewitt and

Tirole (1999); Persson and Tabellini (2000) Elected officials vs nonelected ones: Alesina and Tabellini (2007, 2008); Besley and Coate (2003); Maskin and Tirole (2004) Yardstick Competition – electoral accountability under decentralization: Salmon (1987); Besley and Case (1995); Bordignon, Cerniglia and Revelli (2004); Belleflamme and Hindriks (2005); Besley and Smart (2007)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon Mayor M (for city) and Governor G (for region) are elected in simultaneous elections at the beginning of each period. Majority rule (M at city level, G at region level)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon Mayor M (for city) and Governor G (for region) are elected in simultaneous elections at the beginning of each period. Majority rule (M at city level, G at region level) 2 political parties: L and R

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon Mayor M (for city) and Governor G (for region) are elected in simultaneous elections at the beginning of each period. Majority rule (M at city level, G at region level) 2 political parties: L and R 2 candidates from opposite parties at each elections at each period: incumbent and opponent

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon Mayor M (for city) and Governor G (for region) are elected in simultaneous elections at the beginning of each period. Majority rule (M at city level, G at region level) 2 political parties: L and R 2 candidates from opposite parties at each elections at each period: incumbent and opponent Politicians’ participation constraints are always satisfied. No term limit

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Outline

Big representative city in the region Continuum of individuals; Infinite horizon Mayor M (for city) and Governor G (for region) are elected in simultaneous elections at the beginning of each period. Majority rule (M at city level, G at region level) 2 political parties: L and R 2 candidates from opposite parties at each elections at each period: incumbent and opponent Politicians’ participation constraints are always satisfied. No term limit In office politician i ∈ {M, G} implements policy pi pi = ai + εi

where ai ∈ [0, a] – politician i’s unobservable effort,

εi ∼ N

• 0, σ2

– independent and unobservable noise

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Politicians/Agents Politician i ∈ {M, G} chooses effort ai to maximize Πi (ai) − Ci (ai), where Πi (·) – politician i’s reward, Ci (·) – cost

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Politicians/Agents Politician i ∈ {M, G} chooses effort ai to maximize Πi (ai) − Ci (ai), where Πi (·) – politician i’s reward, Ci (·) – cost Politician i is office-motivated and committed to her political party

Πi (ai, aj) =

• Pri (ai, aj) + λi Prj (ai, aj)

if

S Pri (ai, aj) + λi (1 − Prj (ai, aj))

if

D

where Pri (·) – Pr of being reelected for office i in the coming election

λi ∈ [0, 1] – degree of politician i’s commitment to her party

State S (resp. D) – M and G are members of the same (different) party(ies)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Politicians/Agents Politician i ∈ {M, G} chooses effort ai to maximize Πi (ai) − Ci (ai), where Πi (·) – politician i’s reward, Ci (·) – cost Politician i is office-motivated and committed to her political party

Πi (ai, aj) =

• Pri (ai, aj) + λi Prj (ai, aj)

if

S Pri (ai, aj) + λi (1 − Prj (ai, aj))

if

D

where Pri (·) – Pr of being reelected for office i in the coming election

λi ∈ [0, 1] – degree of politician i’s commitment to her party

State S (resp. D) – M and G are members of the same (different) party(ies) Effort is costly

Ci (ai) =   

a2

i

2ci

if

S

a2

i

2

if

D

where ci > 0

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals I

Some individuals always vote for candidates of the same party for mayor M and governor G

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals I

Some individuals always vote for candidates of the same party for mayor M and governor G A large group of individuals is indifferent between political

• parties. They care about policy outcomes

pM + pG

where pM and pG – observable but not contractible at the end of each period

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals I

Some individuals always vote for candidates of the same party for mayor M and governor G A large group of individuals is indifferent between political

• parties. They care about policy outcomes

pM + pG

where pM and pG – observable but not contractible at the end of each period

These individuals are decisive for outcome of both elections. We call them the voters

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals I

Some individuals always vote for candidates of the same party for mayor M and governor G A large group of individuals is indifferent between political

• parties. They care about policy outcomes

pM + pG

where pM and pG – observable but not contractible at the end of each period

These individuals are decisive for outcome of both elections. We call them the voters Voters coordinate on the same retrospective reappointment rules to reelect M and G – they condition reappointment decision on politicians’ performance pM and pG in the current period and not in any previous period

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals II

Voters can influence politicians’ performance only through the choice of an evaluation rule

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals II

Voters can influence politicians’ performance only through the choice of an evaluation rule Functional space of performance evaluation rules – linear performance evaluation rules (βi, bi) determined by slope βi ≥ 0 and intercept bi ∈ R such that βMβG ≤ 1

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals II

Voters can influence politicians’ performance only through the choice of an evaluation rule Functional space of performance evaluation rules – linear performance evaluation rules (βi, bi) determined by slope βi ≥ 0 and intercept bi ∈ R such that βMβG ≤ 1 Pr of being reelected for office i Pri (ai, aj) = P ({pi (ai) ≥ βipj (aj) + bi})

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals II

Voters can influence politicians’ performance only through the choice of an evaluation rule Functional space of performance evaluation rules – linear performance evaluation rules (βi, bi) determined by slope βi ≥ 0 and intercept bi ∈ R such that βMβG ≤ 1 Pr of being reelected for office i Pri (ai, aj) = P ({pi (ai) ≥ βipj (aj) + bi}) Rules (βi, bi) are required to be sequentially rational

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Voters/Principals III

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing I

At each period

Elections take place. Voters reelect incumbents or not (following reappointment rules chosen in the previous period). State S or D is realized

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing I

At each period

Elections take place. Voters reelect incumbents or not (following reappointment rules chosen in the previous period). State S or D is realized Voters choose reappointment rules (βi, bi) to reward politicians in the coming elections

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing I

At each period

Elections take place. Voters reelect incumbents or not (following reappointment rules chosen in the previous period). State S or D is realized Voters choose reappointment rules (βi, bi) to reward politicians in the coming elections Elected politicians exert efforts aM and aG

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing I

At each period

Elections take place. Voters reelect incumbents or not (following reappointment rules chosen in the previous period). State S or D is realized Voters choose reappointment rules (βi, bi) to reward politicians in the coming elections Elected politicians exert efforts aM and aG Politicians’ performance pM and pG is observed

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing II

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing III

Equilibrium concept – Subgame perfect equilibrium

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Outline Politicians Voters Timing

Model

Timing III

Equilibrium concept – Subgame perfect equilibrium We solve the game backwards

1

Politicians’ efforts aM and aG for rules (βM, bM) and (βG, bG)

2

Voters’ choice of evaluation rules (βM, bM) and (βG, bG)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Politicians’ Reward Politicians’ Effort

Politicians’ Efforts I

Politicians’ Reward

Assume voters use rules (βi, bi)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Politicians’ Reward Politicians’ Effort

Politicians’ Efforts I

Politicians’ Reward

Assume voters use rules (βi, bi) Politician i’s reward is Πi (ai, aj) =                P ({pi (ai) ≥ βipj (aj) + bi}) + λiP ({pj (aj) ≥ βjpi (ai) + bj}) if S P ({pi (ai) ≥ βipj (aj) + bi}) + λi (1 − P ({pj (aj) ≥ βjpi (ai) + bj})) if D

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Politicians’ Reward Politicians’ Effort

Politicians’ Efforts II

Theorem Under linear performance evaluation rules (βM, bM) and (βG, bG), there exists an equilibrium in effort strategies (aM, aG). Furthermore, this equilibrium is defined implicitly by fεi−βiεj (βiaj − ai + bi) =   

aicj+ajciλiβj cicj(1−λiλjβiβj)

if S

ai−ajλiβj 1−λiλjβiβj

if D where fεi−βiεj (·) is the probability density function of εi − βiεj ∼ N

• 0,
• 1 + β2

i

• σ2

.

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Rules’ Choice Intuition

Voters’ Choice of Evaluation Rules I

Voters choose rules (βi, bi) to maximize their expected utility: max

(βM,bM),(βG,bG) E (pM + pG) q

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Rules’ Choice Intuition

Voters’ Choice of Evaluation Rules I

Voters choose rules (βi, bi) to maximize their expected utility: max

(βM,bM),(βG,bG) E (pM + pG) ⇔

max

(βM,bM),(βG,bG) aM + aG q

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Rules’ Choice Intuition

Voters’ Choice of Evaluation Rules I

Voters choose rules (βi, bi) to maximize their expected utility: max

(βM,bM),(βG,bG) E (pM + pG) ⇔

max

(βM,bM),(βG,bG) aM + aG

Theorem There exists a unique equilibrium in rule strategies (β∗

i , b∗ i ) given by

(β∗

i , b∗ i ) =

• (0, a∗

i )

if S

• λj, a∗

i − λja∗ j

• if

D where politicians’ equilibrium efforts a∗

i are equal to

a∗

i =

    

ci √ 2πσ2

if S

1 √ 2πσ2

• 1

q 1+λ2

j

+

λ2

i

√

1+λ2

i

• if

D

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Rules’ Choice Intuition

Voters’ Choice of Evaluation Rules II

Intuition

If state S, voters use absolute performance evaluation rule Pri (ai) = P ({pi (ai) ≥ a∗

i })

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Rules’ Choice Intuition

Voters’ Choice of Evaluation Rules II

Intuition

If state S, voters use absolute performance evaluation rule Pri (ai) = P ({pi (ai) ≥ a∗

i })

If state D, voters use comparative performance evaluation rule Pri (ai, aj) = P

• pi (ai) − a∗

i ≥ λj

• pj (aj) − a∗

j

• Galina Zudenkova

Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Transition Probabilities Stationary Probabilities

Dynamics I

Equilibrium Transition Probabilities

There is a fixed probability Pkl that the city in state k will be next in state l, where k, l ∈ {S, D}

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Transition Probabilities Stationary Probabilities

Dynamics I

Equilibrium Transition Probabilities

There is a fixed probability Pkl that the city in state k will be next in state l, where k, l ∈ {S, D} Lemma The matrix of the equilibrium one-step transition probabilities, P, is equal to P ≡

• PSS

PSD PDS PDD

• =

 

1 2 1 2

1− 1

π

• arctan
• 1

λG

• − arctan (λM)
• 1

π

• arctan
• 1

λG

• − arctan (λM)
• 

 where arctan (·) is an arctangent function.

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Transition Probabilities Stationary Probabilities

Dynamics II

Stationary Probabilities

State S – voters do not split tickets State D – voters split tickets

✏ ✑

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Transition Probabilities Stationary Probabilities

Dynamics II

Stationary Probabilities

State S – voters do not split tickets State D – voters split tickets Theorem The stationary probability that the voters split tickets is independent

• f the initial state, and is equal to

π 3π−2 arctan ✏

1 λG

✑ +2 arctan(λM) ∈

1

3, 1 2

• .

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics I

Null Hypothesis

Null hypothesis. In large municipalities with decisive voters caring about politicians’ performance rather than parties’ ideology, the transitions between the split-ticket and non split-ticket states follow matrix P P ≡

• PSS

PSD PDS PDD

• =

 

1 2 1 2

1− 1

π

• arctan
• 1

λG

• − arctan (λM)
• 1

π

• arctan
• 1

λG

• − arctan (λM)
• 



Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

1995, 1999, 2003 and 2007 elections

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

1995, 1999, 2003 and 2007 elections Two leading Spanish parties PP and PSOE

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

1995, 1999, 2003 and 2007 elections Two leading Spanish parties PP and PSOE Municipalities with more than 15.000 inhabitants (2007 census)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

1995, 1999, 2003 and 2007 elections Two leading Spanish parties PP and PSOE Municipalities with more than 15.000 inhabitants (2007 census) Final sample – 43 cities (≈ 40% of initial sample)

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics II

Data Description

Panel Data on simultaneous municipal and regional elections in six Spanish regions – Castilla-La Mancha, Comunidad de Madrid, Comunitat Valenciana, Islas Baleares, Principado de Asturias and Regi´

• n de Murcia

1995, 1999, 2003 and 2007 elections Two leading Spanish parties PP and PSOE Municipalities with more than 15.000 inhabitants (2007 census) Final sample – 43 cities (≈ 40% of initial sample) Census, number of abstainers, votes to PP, votes to PSOE, votes to other parties for both municipal and regional elections

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics III

Empirical Analysis

Maximum likelihood estimate of the matrix of one-step transition probabilities

• P =
• PSS

1 − PSS

• PDS

1 − PDS

• =
• 0.5774

0.4226 0.6591 0.3409

• Galina Zudenkova

Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics III

Empirical Analysis

Maximum likelihood estimate of the matrix of one-step transition probabilities

• P =
• PSS

1 − PSS

• PDS

1 − PDS

• =
• 0.5774

0.4226 0.6591 0.3409

• Likelihood ratio test (two degrees of freedom, 0.05 percentile)

H0 is not rejected for (λM, λG) such that 0.2185 ≤ 1 π

• arctan

1 λG

• − arctan (λM)
• ≤ 0.4546

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Null Hypothesis Data Analysis

Empirics IV

Empirical Analysis

Range of (λM, λG) for which the null hypothesis is not rejected:

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections.

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

2

If voters split tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period.

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

2

If voters split tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period. Otherwise, absolute performance evaluation rule is used in next period

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

2

If voters split tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period. Otherwise, absolute performance evaluation rule is used in next period

3

Stationary probability that in the long run the principals split tickets is independent on the initial state

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

2

If voters split tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period. Otherwise, absolute performance evaluation rule is used in next period

3

Stationary probability that in the long run the principals split tickets is independent on the initial state, and is lower than stationary probability that they do not split tickets

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Summary and Results

1

We apply implicit incentive approach to split-ticket voting in local simultaneous elections. Principals (voters) influence agents’ (politicians’) performance through the choice of evaluation rules

2

If voters split tickets and if politicians are committed to their political parties, then comparative performance evaluation rule is used in next period. Otherwise, absolute performance evaluation rule is used in next period

3

Stationary probability that in the long run the principals split tickets is independent on the initial state, and is lower than stationary probability that they do not split tickets

4

We find empirical support for model prediction on the equilibrium transition probabilities between split-ticket and non split-ticket states for moderate levels

• f politicians’ commitment to their political parties

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Crucial assumptions Our results rest on fundamental assumptions:

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Crucial assumptions Our results rest on fundamental assumptions:

Voters can compare their utilities from the policies implemented by mayor and governor

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Crucial assumptions Our results rest on fundamental assumptions:

Voters can compare their utilities from the policies implemented by mayor and governor ⇒ they can use comparative performance evaluation rule to reward politicians

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach

Introduction Model Efforts Rule Dynamics Empirics Summary Results Assumptions

Crucial assumptions Our results rest on fundamental assumptions:

Voters can compare their utilities from the policies implemented by mayor and governor ⇒ they can use comparative performance evaluation rule to reward politicians Politicians are committed to their political parties, i.e., they care about overall representation of their party in governing bodies rather than their own reelection prospects

Galina Zudenkova Split-Ticket Voting: An Implicit Incentive Approach