# Pedersen index

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. Pedersen index can be used as an indicator of a change in the party system and to evaluate a change in voter preferences.

## What the index means

   "The net change within the electoral party system resulting from individual vote transfers"

## Construction of the Index

The Pedersen index is calculated as
    $\mathrm {V} ={\frac {1}{2}}\sum _{i=1}^{n}|p_{i,t}-p_{i,t+1}|,$
where $p_{i,t}$ is the percentage of votes for political party $i$ at election $t$ and $p_{i,t+1}$ is the value for the next 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 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 | Blue | Orange | Fuchsia |
| 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 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.
| Country | Year | Pedersen index |
| Argentina | 2011 | 25.1 |
| Austria | 2010 | 7.3 |
| Australia | 2010 | 7.3 |
| Bolivia | 2009 | 35.9 |
| Brazil | 2010 | 18.2 |
| Bulgaria | 2009 | 39.9 |
| Chile | 2009 | 13.9 |
| Colombia | 2010 | 15.9 |
| Costa Rica | 2010 | 29.0 |
| Czech Republic | 2010 | 27.7 |
| Dominican Republic | 2010 | 32.3 |
| Ecuador | 2009 | 33.0 |
| Estonia | 2011 | 32.5 |
| El Salvador | 2012 | 15.5 |
| Germany | 2009 | 8.3 |
| Honduras | 2009 | 7.8 |
| Hungary | 2010 | 25.1 |
| Israel | 2009 | 20.9 |
| India | 2009 | 25.1 |
| Italy | 2008 | 15.2 |
| Japan | 2009 | 14.2 |
| Latvia | 2011 | 36.4 |
| Lithuania | 2012 | 39.7 |
| Macedonia | 2011 | 32.0 |
| Malaysia | 2008 | 13.7 |
| Mexico | 2009 | 21.0 |
| Mongolia | 2008 | 24.3 |
| Netherlands | 2010 | 13.4 |
| Paraguay | 2008 | 25.6 |
| Romania | 2008 | 36.9 |
| Sweden | 2009 | 8.4 |
| Singapore | 2011 | 10.8 |
| South Korea | 2012 | 29.3 |
| Taiwan | 2012 | 16.9 |
| Thailand | 2010 | 27.2 |
| Trinidad and Tobago | 2011 | 25.1 |
| United Kingdom | 2010 | 7.6 |
| United States | 2010 | 3.4 |
| Uruguay | 2009 | 14.6 |
| Venezuela | 2010 | 34.5 |

## Limitations

The "simple and straightforward" way of calculation defined by Pedersen can yield widely varying results in practical cases based on subtle assumptions made by different scholars for "inclusion, aggregation and linkage" due to judgments made on party continuity (or perceived lack thereof).
Both the original Pedersen's method of the 1970s and its improvements suggested in the 2000s (separation of party entry/exit) assume that the parties themselves are stable. Once the splits and mergers become predominant (as is the case, for example, in many countries of the Central Europe in the 21st century, the results provided by the Pedersen's formula will be choices made answering the question like "is the party B a successor to party A?"