December  2011, 15(3): 707-738. doi: 10.3934/dcdsb.2011.15.707

An epidemiological approach to the spread of political third parties

1. 

Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, United States

2. 

University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States

3. 

Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1904, United States

4. 

Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, United States

Received  January 2010 Revised  May 2010 Published  February 2011

Third political parties are influential in shaping American politics. In this work we study the spread of a third party ideology in a voting population where we assume that party members/activists are more influential in recruiting new third party voters than non-member third party voters. The study uses an epidemiological metaphor to develop a theoretical model with nonlinear ordinary differential equations as applied to a case study, the Green Party. Considering long-term behavior, we identify three threshold parameters in our model that describe the different possible scenarios for the political party and its spread. We also apply the model to the study of the Green Party's growth using voting and registration data in six states and the District of Columbia to identify and explain trends over the past decade. Our system produces a backward bifurcation that helps identify conditions under which a sufficiently dedicated activist core can enable a third party to thrive, under conditions which would not normally allow it to arise. Our results explain the critical role activists play in sustaining grassroots movements under adverse conditions.
Citation: Daniel M. Romero, Christopher M. Kribs-Zaleta, Anuj Mubayi, Clara Orbe. An epidemiological approach to the spread of political third parties. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 707-738. doi: 10.3934/dcdsb.2011.15.707
References:
[1]

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California Secretary of State's Office, Voter registration and participation statistics,, Online at \url{http://www.sos.ca.gov/elections/elections_u.htm}, (2009).   Google Scholar

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C. Castillo-Chávez and B. Song, Models for the transmission dynamics of fanatic behaviors,, in, 28 (2003), 155.   Google Scholar

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N. M. Crisosto, C. M. Kribs-Zaleta, C. Castillo-Chávez and S. Wirkus, Community resilience in collaborative learning,, Discrete Continuous Dynam. Systems - B, 14 (2010), 17.   Google Scholar

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B. González, E. Huerta-Sánchez, C. Kribs-Zaleta, A. Ortiz-Nieves and T. Vázquez-Alvarez, Am I too fat? Bulimia as an epidemic,, J. Math. Psychol., 47 (2003), 515.  doi: 10.1016/j.jmp.2003.08.002.  Google Scholar

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R. Huckfeldt and J. Sprague, "Citizens, Politics, and Social Communication: Information and Influence in an Election Campaign,'', Cambridge University Press, (1995).  doi: 10.1017/CBO9780511664113.  Google Scholar

[14]

D. Kowalewski, How movements move: The dynamics of an ecoprotest campaign,, The Social Science Journal, 32 (1995), 49.  doi: 10.1016/0362-3319(95)90019-5.  Google Scholar

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M. W. Macy, Threshold effects in collective action,, Amer. Sociological Review, 56 (1991), 730.  doi: 10.2307/2096252.  Google Scholar

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New York State Board of Elections, Election results,, Online at \url{http://www.elections.state.ny.us/ElectionResults.html}, (2009).   Google Scholar

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D. W. Nickerson, Is voting contagious? Evidence from two field experiments,, Amer. Political Science Review, 102 (2008), 49.  doi: 10.1017/S0003055408080039.  Google Scholar

[24]

P. E. Oliver and G. Marwell, The paradox of group size in collective action: A theory of critical mass, II,, Amer. Sociological Review, 53 (1988), 1.  doi: 10.2307/2095728.  Google Scholar

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Oregon Secretary of State Election Division, Election registration and participation history,, Online at \url{http://www.sos.state.or.us/elections/votreg/regpart.htm}, (2009).   Google Scholar

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Oregon Secretary of State Election Division, Elections history,, Online at \url{http://www.sos.state.or.us/elections/other.info/stelec.htm}, (2009).   Google Scholar

[27]

Pennsylvania Bureau of Commissions, Elections & Legislation, Voter registration statistics archives,, Online at http://www.dos.state.pa.us/elections/cwp/view.asp?a=1310 &q=447072, (2009).   Google Scholar

[28]

Pennsylvania Bureau of Commissions, Elections & Legislation, Elections information,, Online at \url{http://www.electionreturns.state.pa.us/ElectionsInformation.aspx?Function ID=0}, (2009).   Google Scholar

[29]

The Pew Research Center for the People & the Press, Trends in political values and core attitudes: 1987-2007. Political landscape more favorable to Democrats,, Author, (2007).   Google Scholar

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Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World population prospects: The 2008 revision., Online at \url{http://esa.un.org/unpp}, (2009).   Google Scholar

[31]

J. P. Robinson, Interpersonal influence in election campaigns: Two step-flow hypotheses,, Public Opinion Quarterly, 40 (1976), 304.  doi: 10.1086/268307.  Google Scholar

[32]

L. B. Shrestha, Life expectancy in the United States,, (updated August 16, (2006).   Google Scholar

[33]

B. Song, M. Castillo-Garsow, K. R. Ríos-Soto, M. Mejran, L. Henson and C. Castillo-Chávez, Raves, clubs and ecstasy: the impact of peer pressure,, Math. Biosci. Eng., 3 (2006), 249.   Google Scholar

[34]

P. L. Southwell, The politics of alienation: Nonvoting and support of third-party candidates among 18-30-year-olds,, The Social Science Journal, 40 (2003), 99.  doi: 10.1016/S0362-3319(02)00261-6.  Google Scholar

[35]

P. L. Southwell, Nader voters in the 2000 Presidential Election: What would they have done without him?,, The Social Science Journal, 41 (2004), 423.  doi: 10.1016/j.soscij.2004.04.009.  Google Scholar

[36]

R. J. Timpone, Ties that bind: Measurement, demographics, and social connectedness,, Political Behavior, 20 (1998), 53.  doi: 10.1023/A:1024895116980.  Google Scholar

[37]

E. Warren, "U.S. Supreme Court Plurality Opinion, Sweezy v. New Hampshire,", 354 U.S. 234, (1957), 250.   Google Scholar

[38]

J. Wong, The effects of age and political exposure on the development of party identification among Asian American and Latino immigrants in the United States,, Political Behavior, 22 (2000), 341.  doi: 10.1023/A:1010630130895.  Google Scholar

show all references

References:
[1]

L. Bettencourt, A. Cintrón-Arias, D. I. Kaiser and C. Castillo-Chávez, The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models,, Physica D, 364 (2006), 513.  doi: 10.1016/j.physa.2005.08.083.  Google Scholar

[2]

F. Brauer and C. Castillo-Chávez, "Mathematical Models in Population Biology and Epidemiology,'', Springer-Verlag, (2001).   Google Scholar

[3]

California Secretary of State's Office, Statewide election results,, Online at \url{http://www.sos.ca.gov/elections/elections_elections.htm}, (2009).   Google Scholar

[4]

California Secretary of State's Office, Voter registration and participation statistics,, Online at \url{http://www.sos.ca.gov/elections/elections_u.htm}, (2009).   Google Scholar

[5]

C. Castillo-Chávez, Z. Feng and W. Huang, On the computation of $R_0$ and its role on global stability,, in, 125 (2002), 224.   Google Scholar

[6]

C. Castillo-Chávez and B. Song, Models for the transmission dynamics of fanatic behaviors,, in, 28 (2003), 155.   Google Scholar

[7]

N. M. Crisosto, C. M. Kribs-Zaleta, C. Castillo-Chávez and S. Wirkus, Community resilience in collaborative learning,, Discrete Continuous Dynam. Systems - B, 14 (2010), 17.   Google Scholar

[8]

District of Columbia Board of Elections and Ethics, Election results,, Online at \url{http://www.dcboee.org/election_info/election_results/index.asp}, (2009).   Google Scholar

[9]

District of Columbia Board of Elections and Ethics, Voter registration statistics,, Online at \url{http://www.dcboee.org/voter_stats/voter_reg/voter.asp}, (2009).   Google Scholar

[10]

M. Gladwell, "The Tipping Point,'', Little, (2000).   Google Scholar

[11]

B. González, E. Huerta-Sánchez, C. Kribs-Zaleta, A. Ortiz-Nieves and T. Vázquez-Alvarez, Am I too fat? Bulimia as an epidemic,, J. Math. Psychol., 47 (2003), 515.  doi: 10.1016/j.jmp.2003.08.002.  Google Scholar

[12]

M. Granovetter, Threshold models of collective behavior,, Amer. J. Sociol., 83 (1978), 1420.  doi: 10.1086/226707.  Google Scholar

[13]

R. Huckfeldt and J. Sprague, "Citizens, Politics, and Social Communication: Information and Influence in an Election Campaign,'', Cambridge University Press, (1995).  doi: 10.1017/CBO9780511664113.  Google Scholar

[14]

D. Kowalewski, How movements move: The dynamics of an ecoprotest campaign,, The Social Science Journal, 32 (1995), 49.  doi: 10.1016/0362-3319(95)90019-5.  Google Scholar

[15]

M. W. Macy, Threshold effects in collective action,, Amer. Sociological Review, 56 (1991), 730.  doi: 10.2307/2096252.  Google Scholar

[16]

Maine Bureau of Corporations, Elections & Commissions, Election results,, Online at \url{http://maine.gov/sos/cec/elec/prior1st.htm}, (2009).   Google Scholar

[17]

Maine Bureau of Corporations, Elections & Commissions, Voter registration,, Online at \url{http://www.maine.gov/sos/cec/elec/votreg.htm}, (2009).   Google Scholar

[18]

J. Marks, A historical look at Green structure: 1984 to 1992,, Synthesis/Regeneration, 14 (1997), 14.   Google Scholar

[19]

Maryland State Board of Elections, Elections by year,, Online at \url{http://elections.state.md.us/elections/index.html}, (2009).   Google Scholar

[20]

Maryland State Board of Elections, Monthly voter registration activity reports,, Online at \url{http://elections.state.md.us/voter_registration/monthly.html}, (2009).   Google Scholar

[21]

New York State Board of Elections, Enrollment by county,, Online at \url{http://www.elections.state.ny.us/EnrollmentCounty.html}, (2009).   Google Scholar

[22]

New York State Board of Elections, Election results,, Online at \url{http://www.elections.state.ny.us/ElectionResults.html}, (2009).   Google Scholar

[23]

D. W. Nickerson, Is voting contagious? Evidence from two field experiments,, Amer. Political Science Review, 102 (2008), 49.  doi: 10.1017/S0003055408080039.  Google Scholar

[24]

P. E. Oliver and G. Marwell, The paradox of group size in collective action: A theory of critical mass, II,, Amer. Sociological Review, 53 (1988), 1.  doi: 10.2307/2095728.  Google Scholar

[25]

Oregon Secretary of State Election Division, Election registration and participation history,, Online at \url{http://www.sos.state.or.us/elections/votreg/regpart.htm}, (2009).   Google Scholar

[26]

Oregon Secretary of State Election Division, Elections history,, Online at \url{http://www.sos.state.or.us/elections/other.info/stelec.htm}, (2009).   Google Scholar

[27]

Pennsylvania Bureau of Commissions, Elections & Legislation, Voter registration statistics archives,, Online at http://www.dos.state.pa.us/elections/cwp/view.asp?a=1310 &q=447072, (2009).   Google Scholar

[28]

Pennsylvania Bureau of Commissions, Elections & Legislation, Elections information,, Online at \url{http://www.electionreturns.state.pa.us/ElectionsInformation.aspx?Function ID=0}, (2009).   Google Scholar

[29]

The Pew Research Center for the People & the Press, Trends in political values and core attitudes: 1987-2007. Political landscape more favorable to Democrats,, Author, (2007).   Google Scholar

[30]

Population Division of the Department of Economic and Social Affairs of the United Nations Secretariat, World population prospects: The 2008 revision., Online at \url{http://esa.un.org/unpp}, (2009).   Google Scholar

[31]

J. P. Robinson, Interpersonal influence in election campaigns: Two step-flow hypotheses,, Public Opinion Quarterly, 40 (1976), 304.  doi: 10.1086/268307.  Google Scholar

[32]

L. B. Shrestha, Life expectancy in the United States,, (updated August 16, (2006).   Google Scholar

[33]

B. Song, M. Castillo-Garsow, K. R. Ríos-Soto, M. Mejran, L. Henson and C. Castillo-Chávez, Raves, clubs and ecstasy: the impact of peer pressure,, Math. Biosci. Eng., 3 (2006), 249.   Google Scholar

[34]

P. L. Southwell, The politics of alienation: Nonvoting and support of third-party candidates among 18-30-year-olds,, The Social Science Journal, 40 (2003), 99.  doi: 10.1016/S0362-3319(02)00261-6.  Google Scholar

[35]

P. L. Southwell, Nader voters in the 2000 Presidential Election: What would they have done without him?,, The Social Science Journal, 41 (2004), 423.  doi: 10.1016/j.soscij.2004.04.009.  Google Scholar

[36]

R. J. Timpone, Ties that bind: Measurement, demographics, and social connectedness,, Political Behavior, 20 (1998), 53.  doi: 10.1023/A:1024895116980.  Google Scholar

[37]

E. Warren, "U.S. Supreme Court Plurality Opinion, Sweezy v. New Hampshire,", 354 U.S. 234, (1957), 250.   Google Scholar

[38]

J. Wong, The effects of age and political exposure on the development of party identification among Asian American and Latino immigrants in the United States,, Political Behavior, 22 (2000), 341.  doi: 10.1023/A:1010630130895.  Google Scholar

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