Pedersen index explained

The Pedersen index is a measure of political volatility in party systems. It was described by Mogens Pedersen in a paper published in 1979 entitled The Dynamics of European Party Systems: Changing Patterns of Electoral Volatility.^[1]

What the index means

"The net change within the electoral party system resulting from individual vote transfers"^[2]

Construction of the Index

The Pedersen index is calculated as

V = (1)/(2) \sum ^{n} _{i =1} | p _{i,t} - p _{i,t+1} |,   

where

p _{i,t} is the percentage of party political party i at election t and p _{i,t+1} for the consecutive election. To calculate the index, the percentage gains of the winning parties must be determined. The resulting index will be between 0 (no parties gained, and thus no parties lost either) and 100 (all the parties from the last election were reduced to zero votes), because for every gain there is an equal (in terms of percentage of votes) loss. In other words, the index is equal to the net percentage of voters who changed their votes. ("Net percentage," because if the only change is a Party A voter switching to Party B, and a Party B voter switching to Party A, there is no net volatility.)The index can also be constructed by summing the absolute values of all gains and all losses, and dividing this total by two.

The political volatility measured by the Pedersen index differs from the political volatility when parliamentary seats are considered due to the differing seats-to-votes ratios. The Pedersen index can overestimate the political volatility for countries with newly formed parliamentary groups made of previously existing political parties. Other measures^[3] differ in their estimates of political volatility.

Example

Assume that in the first election the Blue Party won 65%, the Orange Party won 25%, and the Fuchsia Party won 10%. Furthermore, assume that in the second election the Blue Party won 65%, the Orange Party won 15%, and the Fuchsia Party won 20%.

Election\Party
1st	65%	25%	10%
2nd	65%	15%	20%
Gain/Loss	0	-10	10

The index would be equal to Blue gains (none) plus Orange's loss (10% since we do not consider sign differences) plus Fuchsia gains (10%). We then multiply it by 1/2 or divide by 2 for a total volatility of 10%.

If all three parties had disappeared in the next election, and been replaced by the Red Party (75%) and the Black Party (25%), the volatility would have been 100%: The first three lose all (100%) + the Red Party gaining 75% and the Black Party 25% since the previous election (when they both received no votes.) 100+100 = 200 -> divide by 2 = 100

Countries

The Pedersen indices for individual countries^[4] are listed below, only the last available index is shown. The Pedersen index tends to decrease for some countries with increasing number of consecutive elections.^[4]

Country	Year	Pedersen index
	2011	25.1
	2010	7.3
	2010	7.3
	2009	35.9
	2010	18.2
	2009	39.9
	2009	13.9
	2010	15.9
	2010	29.0
	2010	27.7
	2010	32.3
	2009	33.0
	2011	32.5
	2012	15.5
	2009	8.3
	2009	7.8
	2010	25.1
	2009	20.9
	2009	25.1
	2008	15.2
	2009	14.2
	2011	36.4
	2012	39.7
	2011	32.0
	2008	13.7
	2009	21.0
	2008	24.3
	2010	13.4
	2008	25.6
	2008	36.9
	2009	8.4
	2011	10.8
	2012	29.3
	2012	16.9
	2010	27.2
	2011	25.1
	2010	7.6
	2010	3.4
	2009	14.6
	2010	34.5

References

1. http://janda.org/c24/Readings/Pedersen/Pedersen.htm Pedersen's paper
2. W. Ascher and S. Tarrow, 'The Stability of Communist Electorates: Evidence from a Longitudinal Analysis of French and Italian Aggregate Data', American Journal of Political Science, 19/3 (1975), 48o-i.
3. https://dx.doi.org/10.7802/1112 Emanuele, Vincenzo. "Dataset of Electoral Volatility and its internal components in Western Europe (1945-2015)." (2015).
4. Web site: Institutionalization of party systems: a cross-regional approach using the Weighted Volatility Index, Eduardo Olivares Concha, Prepared for the Political Studies Association 64th Annual International Conference, Manchester, 2014 .