Weighted Variance

Description

The weighted variance of party ideology scores was the first measure used to measure ideological polarization. It was first used by Taylor and Herman (1971) and is still very popular. The variance formula includes weights to account for the different sizes of the parties, which some operationalize as seat shares (e.g., Taylor and Herman 1971, Hazan 1997), while others use vote shares (e.g., Béjar et al. 2020, Sigelman and Yough 1978). The measure has been applied to a variety of data sources, including the CSES, WVS, and MARPOR.

Operationalization

The formula for the weighted variance is as follows:

$$V= \sum_{i=n}^N f_i (x_i - \bar{x})^2$$

where $N$ is the number of parties, $f_i$ is the vote or seat share of party $i$, $x_i$ is the ideological position of party $i$, and $\bar{x}$ is the weighted average of the positions of all parties. If survey data are used, $x_i$ is determined as the average of all respondents’ rankings of party $f$.

polaR

# Import Data
cses_imd <- polaR_import(source = "cses_imd", path = "path/to/dataset.dta")

# Where different issue dimensions are available, 'issue' can be issued to specify the one to use
variance_data <- variance(cses5,
						 issue = "leftright")

Visualization

Use cases

Publications that use this measure: