642 final project

Abstract

Leaning primarily on Duverger’s Law, which credits minor party votes as wasted momentum, current research on institutional obstacles to minor party voting largely overlooks the influence of constituency size. This research reexamines the electoral hindrances that minor parties face when competing against the two dominant political parties. Specifically, I hypothesize there is a negative relationship between constituency size and minor party vote share. This thesis adopts an institutional approach to explain the success of minor parties in constituencies of varying size. In the empirical models, I will control for state one-party dominance, if an election is missing a major party candidate, state ballot access laws and whether states allow fusion practices, which permit candidates to run under both a minor and a major political party label. The intent is to isolate the effects of constituency size. Using Generalized Least Squares (GLM) Regression and archival election data from the Clerk of the House of Representatives and the Secretary of State offices from each of the fifty states, this research finds evidence that smaller constituencies improve minor party candidate success. The findings suggest smaller constituencies can neutralize other institutional barriers to electoral prowess put in place by the two-party duopoly or Democratic and Republican Party dominance.

Hypothesis

H1: A larger constituency size predicts less minor party voting.

Model

\(Minor Party Voting = \beta_{0} + \beta_{1}Constituency Size + \beta_{2}Fusion + \beta_{3}Ballot Access+ \beta_{4}MajorPartyMissing + \beta_{5}OnePartyDominance+\epsilon\)

Independent variable (X): Constituency Size (logged)

Dependent variable (Y): Minor Party Vote Share (minor party voting)

Variables

Variable Name	Description
popsize	The main independent variable. Used to measure constituency size. Uses Census data from 2008-2022 (2000,2010,& 2020)
percent_nonmajor_voting	The main dependent variable. It is the number of nonmajor party voting in relation to the total votes for a given election (as percent of the total election votes).
fusion	Represents electoral fusion. It is a three-way coded variable. States coded with a “1” consist of full fusion voting (New York and Connecticut). The three states that limit fusion to presidential candidates (Vermont, Oregon, and California) are coded as a “0.5”. Lastly, the two states that limit fusion to judicial elections (Maryland and Pennsylvania) are coded with a “0.25”
ballotaccess_over1percsignature	Simplifies the ballot access data into a dummy variable. This variable looks at the “ballotaccessAverage” variable, and when a state average is over 1 percent, it is coded with a “1”.
major_party_missing	This is a dummy variable, where “1” represents a major party missing from a given race. This variable is meant to account for the nature of race when either a Democrat or a Republican is not running
one_party_dominance	This variable captures party dominance in each of the states. Presidential races are used to calculate this number. Using the most recent presidential election race for each of the years in this dataset (2008-2022). I take the percentage of votes each of the major candidates (Dem and Rep) receive in the state’s most recent presidential election. This variable represents the difference between the percentage of votes for the Democratic and Republican presidential candidates.

Minor Party Vote Share Distributions

Regression Tables

Main Regression used in paper

Bivariate Model

	(1)
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept)	28.632***
	(5.500)
log(popsize)	-1.551***
	(0.367)
Num.Obs.	512
R2	0.034
AIC	3713.4
BIC	3726.1
Log.Lik.	-1853.690
F	17.833
RMSE	9.04

Multivariate Model- Random Effects

	(1)	(2)
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept)	25.286***	22.584***
	(6.855)	(5.640)
log(popsize)	-1.349**	-1.171***
	(0.432)	(0.355)
fusion	4.760**	4.670**
	(1.830)	(1.650)
ballotaccessAverage	-0.389	-1.096*
	(0.743)	(0.542)
major_party_missing	30.520***	29.071***
	(2.382)	(1.921)
one_party_dominance	-0.057	-0.008
	(0.040)	(0.033)
Num.Obs.	252	508
R2	0.449	0.353
R2 Adj.	0.438	0.346
AIC	1662.8	3488.9
BIC	1687.5	3518.5
RMSE	6.38	7.40

Appendix: Robustness check regressions

Multivariate Model- Within Effects

	(1)	(2)
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
log(popsize)	-1.336**	-1.205***
	(0.434)	(0.357)
fusion	4.545*	4.520**
	(1.837)	(1.660)
ballotaccessAverage	-0.363	-1.082*
	(0.744)	(0.544)
major_party_missing	30.791***	29.213***
	(2.391)	(1.925)
one_party_dominance	-0.055	-0.011
	(0.040)	(0.033)
Num.Obs.	252	508
R2	0.455	0.358
R2 Adj.	0.437	0.342
AIC	1657.7	3479.4
BIC	1678.9	3504.8
RMSE	6.34	7.34

Multivariate Model- Between Effects

	(1)	(2)
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept)	27.925***	26.560**
	(7.342)	(8.036)
log(popsize)	-1.517**	-1.395**
	(0.462)	(0.500)
fusion	5.379**	6.043**
	(1.952)	(2.220)
ballotaccessAverage	-0.590	-1.449+
	(0.794)	(0.801)
major_party_missing	27.482***	32.581***
	(5.208)	(5.662)
one_party_dominance	-0.045	-0.029
	(0.042)	(0.050)
Num.Obs.	102	102
R2	0.384	0.405
R2 Adj.	0.352	0.374
AIC	592.0	598.5
BIC	610.4	616.9
RMSE	4.11	4.25

Hausman Tests

I use Hausman Tests to check if random or fixed effects is more appropriate. If the p-value is significant at (<0.5) then I should use fixed effects. If it is NOT significant, then random effects should be used

Hausman test with small model 2016-2022 (WITHIN)

## 
##  Hausman Test
## 
## data:  percent_nonmajor_voting ~ log(popsize) + fusion + ballotaccessAverage +  ...
## chisq = 3.026, df = 5, p-value = 0.696
## alternative hypothesis: one model is inconsistent

Hausman test with large model 2008-2022 (WITHIN)

## 
##  Hausman Test
## 
## data:  percent_nonmajor_voting ~ log(popsize) + fusion + ballotaccessAverage +  ...
## chisq = 3.5376, df = 5, p-value = 0.6177
## alternative hypothesis: one model is inconsistent

Bivariate Figure

## `geom_smooth()` using formula = 'y ~ x'