Estimating preferences for the performing arts from referendum votes

Abstract

The value of the performing arts to the population can be elicited from referendum outcomes. The analyses typically rely on the (strong) assumption of full voter turnout. I show theoretically that when turnout is ignored, coefficients of variables related positively (negatively) to turnout yield upward (downward)-biased coefficients. For an empirical application, I use the example of a 2009 referendum in the Swiss canton of St.Gallen regarding the public financing of the local theater. Taking into account the turnout decision yields statistically but not economically different estimates. Bayesian model averaging suggests that income, old age, political orientation, and travel time to the theater are most closely related to the vote outcome. The analysis is complemented by comparing voter characteristics from post-ballot surveys with municipal characteristics. Voters tend to exhibit characteristics which are positive drivers of support for the referendum. This suggests that support for cultural spending among voters might be larger than among the overall population.

Appendix

1.1 Proof

The probability of voting for referendum $r$ is:

$$\begin{aligned} {\mathrm{Prob}}({\mathrm{vote}}=r)=\frac{e^{\beta _r X}}{e^{\beta _r X}+e^{\beta _q X}e^{\gamma W}} \end{aligned}.$$

(5)

Normalizing $\beta _q=1$, dividing everything by $e^{\beta _r X}$ and rearranging yields:

$$\begin{aligned} {\mathrm{Prob}}({\mathrm{vote}}=r)=\frac{1}{1+e^{\gamma W-\beta _r X}} \end{aligned}.$$

(6)

I define $Z=\beta _r X - \gamma W$ and write the voting probability as ${P={\mathrm{Prob}}({\mathrm{vote}}=r)}$. Solving Eq. (6) for $e^Z$ results in:

$$\begin{aligned} e^Z=\frac{P}{1-P} \end{aligned}.$$

(7)

Taking the natural logarithm on both sides and substituting back for $Z$ yields:

$$\begin{aligned} \log \left( \frac{P}{1-P}\right) =\beta _rX-\gamma W \end{aligned}.$$

(8)

To account for the fact that individual voting probabilities are unknown to the researcher and only aggregate voting data at municipal level are available, sample means are used for the estimation. Denote the number of citizens in municipality $m$ by $c_m$ and the number of yes votes by $y_m$. The probability of voting yes in a given municipality is then defined as $\hat{P}_m =y_m/c_m$. Substituting into Eq. (8) yields the following estimation equation:

$$\begin{aligned} \log \left( \frac{\hat{P}_m}{1-\hat{P}_m}\right) =\hat{\beta }_rX_m-\hat{\gamma } W_m+\epsilon _m \end{aligned}.$$

(9)

$X_m$ and $W_m$ are explanatory variables at municipal level related to vote choice and turnout. $\epsilon _m$ denotes the error term.

1.2 Data sources

See Tables 5 and 6.

Table 5 Overview of variables and data sources

Table 6 Correlation coefficients of all variables

1.3 Turnout evidence from federal post-ballot surveys

This section complements the main analysis and compares voter characteristics with municipal averages of socioeconomic variables. After all federal voting days in Switzerland post-ballot surveys, the VOX surveys are conducted. Randomly selected citizens are contacted by telephone and asked about their voting decisions as well as a wealth of personal information. The questions only concern federal referenda, so the survey cannot be used to analyze preferences for the cantonal vote. However, the turnout decision on a given voting day is highly correlated between the various measures taking place on the same day. The survey can therefore be utilized to explore the characteristics of the voting population and compare it to the total population.

Income, education, and age are variables collected during the survey which coincide with variables used in the above regressions. I therefore compare the descriptive statistics from municipal data with the ones from survey respondents. I use only respondents who reported to have voted. Income is reported in five categories in the survey. I translate the average municipal monthly income into the five categories to make it comparable to the survey.¹⁵

The numbers are presented in Table 7. The first three columns refer to respondents from German-speaking cantons. While these voters need not be representative of the canton of St.Gallen, this sample selection ensures a sufficient number of observations. The following three columns are based on respondents from the canton of St.Gallen. The last three repeat municipal used in the aggregate analysis for comparability. T-statistics for the hypothesis that sample averages are equal to the cantonal averages are in parentheses. Comparing the German-speaking sample with the cantonal descriptives shows a clear trend: voters on the September 27, 2009, were significantly richer, better educated, and older than the average population. The comparison for the sample from the canton St.Gallen should be interpreted carefully because the number of observations drops from more than 300 to only 30. While the values of all three variables are larger in the St.Gallen sample than among average citizens, the difference is significant for income and marginally insignificant for the share of older people.

Table 7 Descriptives of voter characteristics

The exercise provides suggestive evidence specifically for the voting day the St.Gallen Theater referendum took place that voters differed from average citizens in terms of variables that are positively related to preferences for cultural spending. Therefore, voters could be expected to be more supportive of cultural spending than average citizens.