Generating party systems

Chris Hanretty

chris.hanretty@rhul.ac.uk

Royal Holloway, University of London

“What I cannot create, I do not understand”

Laver and Sergenti (2011)

Lehrer and Schumacher (2018)

Today

• A mechanism for simulating realistic party systems where parties have:
  • (seat or vote) shares
  • positions on a left-right spectrum
• Why?
  • Intrinsic value
  • Generate expectations for other things (congruence, polarization)

Outline

• Four mechanisms: positions are
  • weakly centred on the position of the average voter
  • system autoregressive / repulsive
  • increasingly variable / eccentric
  • initially bimodal
• Training data
• Generating systems
• Audience participation!

Mechanisms

The average voter

\[ \theta \sim N(\alpha + \beta \cdot \tilde{x}, \sigma) \]

\[ \theta \sim N(\color{#EB641E}{\alpha} + \beta \cdot \tilde{x}, \sigma) \]

\[ \theta \sim N(\alpha + \color{#EB641E}{\beta} \cdot \tilde{x}, \sigma) \]

\[ \theta \sim N(\alpha + \beta \cdot \color{#EB641E}{\tilde{x}}, \sigma) \]

\[ \theta \sim N(\alpha + \beta \cdot \tilde{x}, \sigma) \]

\[ 0 \le \beta \le 1 \]

“System” autoregressive

“Parties are repulsed away from the share-weighted average position of all parties larger than them”

System autoregressive

System autoregressive

\[ \theta^{\ast{}}_j = \frac{\sum_{i=1}^j s_i \theta_i}{\sum_{i=1}^j s_i} \]

		Party position		System position		Lagged system position
Party	Seat share	θ	SE(θ)	θ*j	SE(θ*j)	θ*j-1	SE(θ*j-1)
Conservative	0.523	0.987	0.145	0.987	0.145	NA	NA
Labour	0.368	-0.870	0.206	0.221	0.120	0.987	0.145
SNP	0.089	-0.846	0.179	0.124	0.111	0.221	0.120
Liberal Democrats	0.013	-0.211	0.168	0.120	0.109	0.124	0.111
Plaid Cymru	0.005	-0.937	0.178	0.115	0.109	0.120	0.109
UKIP	0.002	1.580	0.175	0.117	0.109	0.115	0.109
Green	0.002	-1.319	0.220	0.115	0.108	0.117	0.109

System autoregressive

\[ \begin{align} \theta_j \sim N(&\alpha + ... + \\ &\rho \cdot{} \theta^{\ast{}}_{j-1} + ..., \\ &\sigma) \end{align} \]

\[ \begin{align} \theta_j \sim N(&\alpha + ... + \\ &\color{#EB641E}{\rho} \cdot{} \theta^{\ast{}}_{j-1} + ..., \\ &\sigma) \end{align} \]

\[ -1 \le \rho \le 0 \]

Increasing variability

Increasing variability

\[ \log(\sigma_j) = f(s_j) \]

Initial bimodalism

• Downs is pretty wrong
• The positions of largest parties are on average “moderately far” from the position of the median voter
• When dealing with standardized units, it’s about +/- 0.75 units

Initial bimodalism

• Mixture model with two component distributions:
  • Left distribution: \(\mu_L = \alpha^{F} + \beta^{F} \cdot x - \omega\)
  • Right distribution: \(\mu_R = \alpha^{F} + \beta^{F} \cdot x + \omega\)
• Distributions also have modelled variances:
  • \(\sigma = f(s_1)\)
• Can model the mixing parameter, but it’s pretty close to 50:50

Recap

• Party positions are drawn from normal distributions
• The mean of this distribution depends on:
  • some overall intercept (\(\alpha\))
  • the position of the avg. voter (\(x\)) times coefficient \(\beta\)
  • the share-weighted avg system position for larger parties (\(\theta^{\ast{}}_{j-1}\)), times some repulsion parameter \(\rho\)
• The variance of this distribution depends on the share
• The largest party’s position comes from a mixture of two normal distributions

Training

Party positions

• Castles and Mair (1984)
• Huber and Inglehart (1995)
• Laver and Hunt (1992) / Benoit and Laver (2006)
• Jolly et al. (2022) / Norris, Ruiz, and Williams (2023)
• Düpont et al. (2022)
• Lehmann et al. (2023)
• Herrmann and Döring (2023)

Strategy: combine these sources using a dynamic latent trait model (Reuning, Kenwick, and Fariss 2019)

Outputs: standardized measures on an economic left-right scale which approximately follow a standard normal distribution (mean ~ 0, SD ~ 1)

Voter positions

Trivia question: what, on a 0-10 scale, is the position of the median voter in the 2019 Australian election?

Trivia question: what, on a 0-10 scale, is the position of the median voter in the 2018 Swedish election?

Trivia question: what, on a 0-10 scale, is the position of the median voter in the 1988 Swedish election?

Trivia question: what, on a 0-10 scale, is the position of the median voter in the 1987 Australian election?

Voter positions: intuition

“You 1987-Aussie, you put this party - score +0.63 - at position 6; you put this party [score -0.2] at position 3, so when you say you are a five, that probably means you’re at 0.2 yourself”

Voter positions: implementation

• Estimate a multilevel ordinal probit model
• Judgements of multiple parties “nested within” respondents
• Each respondent has separate intercept and slope
• Conditional on model parameters and their self-placement, get the MLE of the voter’s position
• Run ~300 models, one per country/year

Models of party positions

• Estimate a model which includes:
  • different components (first parties, all other parties)
  • heteroskedasticity (modelled variances)
  • measurement error
  • share weights
• … on 3,000 party positions, to find out about parameters
• parties two to ???: \(\alpha\), \(\beta\), \(\rho\)
• largest-parties: \(\alpha^F\), \(\beta^F\), \(\omega\)

Model results

	Seat share weights
α: Intercept	0.243 [0.142, 0.343]
αF: Intercept, first party	0.063 [-0.027, 0.153]
β: Mean voter position	0.890 [0.601, 1.176]
βF: Mean voter position	0.462 [0.203, 0.725]
ρ: Repulsion	-0.922 [-1.008, -0.832]
ω: Increment	0.730 [0.678, 0.781]
p: Mixing parameter	0.499 [0.420, 0.577]
δ1: Intercept on log SD	0.038 [-0.090, 0.170]
δ2: Coef. of share² on log SD	-8.401 [-10.444, -6.408]
δF1;: Intercept on log SD	-0.636 [-0.934, -0.313]
δF2: Coef. of share² on log SD	-3.532 [-5.452, -1.640]
σk: SD, country intercepts	0.203 [0.120, 0.292]
σkt: SD, country-by-year intercepts	0.026 [0.002, 0.065]
Num.Obs.	2406
LOOIC	568.439
SE.LOOIC.	17.173
max.Rhat.	1.004
mean.Rhat.	1.001

Generating

N = 7

 

 

 

 

 

 

Making good guesses

• √(LB × UB)
• = √(1 × 7)
• = 37.7%

Making good guesses

• R = 1 - 0.378
• LB = R / 6; UB = R
• √(LB × UB)
• = √(R/6 × R)
• = 0.254

Making good guesses

• R = 1 - 0.378 - 0.254
• LB = R / 5; UB = R
• √(LB × UB)
• = √(R/5 × R)
• = 0.165

Making good guesses

• R = 1 - 0.378 - 0.254 - 0.165
• LB = R / 4; UB = R
• √(LB × UB)
• = √(R/4 × R)
• = 0.102

Making good guesses

• R = 1 - 0.378 - 0.254 - 0.165 - 0.102
• LB = R / 3; UB = R
• √(LB × UB)
• = √(R/3 × R)
• = 0.059

Making good guesses

• R = 1 - 0.378 - 0.254 - 0.165 - 0.102 - 0.059
• LB = R / 2; UB = R
• √(LB × UB)
• = √(R/2 × R)
• = 0.03

Making good guesses

• R = 1 - 0.378 - 0.254 - 0.165 - 0.102 - 0.059 - 0.03
• LB = R / 1; UB = R
• √(LB × UB)
• = √(R/1 × R)
• = 0.013

Making probabilistic guesses

• We can make these the mean predictions for a Dirichlet distribution
• We can then adjust the precision to make simulated shares further or closer to these means
• For details, see Cohen and Hanretty (2024)

Flipping the logic

• First generate the shares
• Then generate positions consistent with the shares
• Explanatory sequence != causal sequence
• In practice, parties adopt positions before they win any votes
• Compare to models of “votes from seats”

Audience participation

Example 1

Example 2

Example 3

Generally…

I asked 22 EPOP attendees to evaluate seven fictitious countries’ party systems.

They had to say whether these party systems were fake or real.

On average, half were fake, half real.

Across 154 guesses, the average proportion of correct guesses was 54.9%.

This is not significantly different from the proportion one would get by chance (50%) (95% CI: 44.8 - 65).

Conclusions

• Party systems can be generated by:
  • generating shares
  • generating positions conditional on shares
• These party systems seem to be plausible / realistic
• These party systems can be used to generate expectations about other properties of party systems

References

Benoit, Kenneth, and Michael Laver. 2006. Party Policy in Modern Democracies. Routledge.

Castles, Francis, and Peter Mair. 1984. “Left-Right Political Scales: Some ’Expert’ Judgements.” European Journal of Political Research 12 (1): 73–88.

Cohen, Denis, and Chris Hanretty. 2024. “Simulating Party Shares.” Political Analysis 32 (1): 140–47.

Düpont, Nils, Yaman Berker Kavasoglu, Anna Lührmann, and Ora John Reuter. 2022. “A Global Perspective on Party Organizations. Validating the Varieties of Party Identity and Organization Dataset (v-Party).” Electoral Studies 75: 102423.

Herrmann, Michael, and Holger Döring. 2023. “Party Positions from Wikipedia Classifications of Party Ideology.” Political Analysis 31 (1): 22–41.

Huber, John, and Ronald Inglehart. 1995. “Expert Interpretations of Party Space and Party Locations in 42 Societies.” Party Politics 1 (1): 73–111.

Jolly, Seth, Ryan Bakker, Liesbet Hooghe, Gary Marks, Jonathan Polk, Jan Rovny, Marco Steenbergen, and Milada Anna Vachudova. 2022. “Chapel Hill Expert Survey Trend File, 1999–2019.” Electoral Studies 75: 102420.

Laver, Michael, and W Ben Hunt. 1992. Policy and Party Competition. Routledge.

Laver, Michael, and Ernest Sergenti. 2011. Party Competition: An Agent-Based Model. Vol. 20. Princeton University Press.

Lehmann, Pola, Simon Franzmann, Tobias Burst, Sven Regel, Felicia Riethmüller, Andrea Volkens, Bernhard Weßels, and Lisa Zehnter. 2023. “The Manifesto Data Collection. Manifesto Project (MRG/CMP/MARPOR). Version 2023a.” Berlin: Wissenschaftszentrum Berlin für Sozialforschung (WZB); Göttingen: Institut für Demokratieforschung (IfDem). https://doi.org/10.25522/manifesto.mpds.2023a.

Lehrer, Roni, and Gijs Schumacher. 2018. “Governator Vs. Hunter and Aggregator: A Simulation of Party Competition with Vote-Seeking and Office-Seeking Rules.” Plos One 13 (2): e0191649.

Norris, Pippa, Jorge Ruiz, and Luke Williams. 2023. “Global Party Survey 2019.” https://dataverse.harvard.edu/dataverse/GlobalPartySurvey.

Reuning, Kevin, Michael R Kenwick, and Christopher J Fariss. 2019. “Exploring the Dynamics of Latent Variable Models.” Political Analysis 27 (4): 503–17.