The voting power of political agents can be measured in many ways. Usually, the simple count of votes is not good enough. For example, if there are many parties in the parliament with various shares of votes, a simple majority rule is used and none of the parties has half of the votes, then the final outcome is a question of coalition building. However, like Henning and Uusikylä (1995, 6-10) point out, the task of transforming the individual preferences of political agents to a commonly chosen policy outcome is not a simple task. One measure of voting power used in these kinds of situations is a measure introduced by Shapley and Shubik (1954). The Shapley-Shubik measure is based on the idea of forming all possible coalitions parties can build and then calculating for each party the number of times these parties are in a crucial position in a coalition i.e. if they leave the coalition it is not a winning coalition anymore. The Shapley-Shubik measure has been applied in variety of decision making settings (see e.g. König 1993; Pappi et al. 1995; Widgren 1995).
As an equation the Shapley-Shubik voting power for party i (øi) is calculated as follows:
where s is the number of parties in a coalition S, n is the number of parties in the parliament and is 1 if the coalition S of which i is member is a winning coalition, but is not a winning coalition without i, and zero otherwise (Coleman 1986, 196). The summation is taken over all possible coalitions in which i is a member.
The Shapley-Shubik measure has some properties that make it very useful (see Coleman 1986, 193-195). One of them is that if the number of votes in the decision making body add up to one (or the vote shares will at least) then the sum of the measure of power of members is also one. Another useful feature of the Shapley-Shubik measure is that these measures can be added if there are two decision phases e.g. in a case when a decision has to pass two houses of parliament. This feature will be used next when the voting power matrix for agents is determined.
König and Bräuninger (1996) extend the Shapley-Shubik value to multi-chamber voting situations. They compare voting procedures in U.S. and German parliaments. Their methodology can be applied in the Finnish case, although the Finnish Parliament has only one chamber. However, if the agenda setting power of the government is included, the voting situation can be analysed as a two-chamber problem. However, before the examination of the Finnish case is presented, an example how the Shapley-Shubik values in multi-chamber situation are calculated is shown.
The Shapley-Shubik power measure can be calculated with the use of all possible sequences players can be put into. For example, if there are three players in a voting situation, these players can cast their votes in 3!=6 different order. The Shapley-Shubik value can be calculated by looking at each sequence and examining which of the players is a pivotal player. A pivotal player is a player in such a place in a sequence that he/she can cast the decisive vote, if all the players preceding him/her vote for 'yes' and all the players after him/her vote for 'no'. In the example of three players it is the second player in a sequence that is pivotal. Because the player before him/her votes 'yes' and the one after him votes 'no', the second player can decide the outcome. The total Shapley-Shubik value for a player is the number of sequences in which this player is pivotal divided by the number of sequences.
Table 7 shows an example how this simple way of calculating Shapley-Shubik values can be extended to multi-chamber situation. In this example there is a parliament which has two chambers and a simple majority in both chambers is needed to pass new legislation. In this parliament the party discipline is strong and the parties vote always as a group. The first chamber of the parliament is controlled by party A, which has all the votes in this chamber. The second chamber consists of three parties B, C and D which all have 1/3 of the votes. These four parties can be arranged into 4!=24 different sequences. All these sequences are shown in Table 7. In each sequence the pivotal party is marked with bold letter. For example, in the first voting sequence ABCD, party A is pivotal, because it can obstruct any decisions. In the sequence BCAD, party C is pivotal, because if C votes 'no' the law will be rejected (remember that in a sequence all players preceding the pivotal player vote 'yes' and all players after the pivotal player vote 'no'). The overall voting power is the number of pivotal positions divided by the number of sequences. In this case party A's voting power is 0.5 and the voting power of B, C and D is 0.167.
A B C D C A B D
A B D C C A D B
A C B D C B A D
kxkxkxk
A C D B C B D A
A D B C C D A B
A D C B C D B A
B A C D D A B C
B A D C D A C B
B C A D D B A C
B C D A D B C A
B D A C D C A B
B D C A D C B A
Player A is pivotal in 12 sequences out of 24. Voting power of
player A is 12/24=0.5.
Players B, C and D are each pivotal in 4 sequences out of 24.
Voting power of each of these players is 4/24=0.167.
Table 7. An example of calculating Shapley values. The pivotal player is in bold.
Using the summation rule mentioned earlier, it is possible to add up parties power measures. Using the same example, it is possible to calculate the power of each chamber, which is simply the sum voting powers of all parties in that chamber. In the example the voting power is 0.5 for both chambers. Furthermore, in a situation when a party is represented in both chambers its total voting power is simply a sum of its voting power in each of the chambers. If the player A in the earlier example is a fraction of same party as player B in the other chamber, the total voting power of this party is 0.5+0.167=0.667.
Pappi et. al (1995) use this procedure to calculate voting power in a parliament using three sets of different assumptions. They call these models Legislative model, Policy Leadership model and Party Government model. In the following analysis these models are adapted to the Finnish institutional setting and Shapley-Shubik voting power measures are calculated for the agents i.e. parties in the Finnish Parliament.
In the Finnish Parliament, Eduskunta, the party discipline is strong. Thus, it is reasonable to think of parliamentary parties as unitary actors in parliament voting situations. It is assumed that the legislative process consists of two stages. First, the government decides if a legislative proposal is given to the parliament or not. In the second stage, the legislative proposal goes through the parliament procedures and ends up (if not rejected before) in the final voting situation in which it is decided if the proposal will be enacted as a new law or not. Thus, there are two 'gates' a proposal must pass before it is accepted as a new law.
The first stage of this process (the government decision) can be seen as voting situation in which each party in government has as many votes as it has ministers in the government. The government decision are made according to the simple majority rule (Nousiainen 1988, 228). If the proposal passes this vote, it will be given to the Parliament. The Shapley-Shubik measures for this first stage is calculated using the number of votes (i.e. ministers) each government party has. Of course, the opposition parties have no voting power in this stage.
The second stage is more problematic. Until recently, one third of all parliament members could postpone an ordinary legislative proposal to be considered anew by parliament (Anckar 1992, 161). This second consideration did not take place in the next annual parliamentary session, but in the session that followed thereafter. A postponed legislative proposal became law only if it was adopted unchanged by parliament. This postponement rule was enacted originally to protect the constitution from socialist take-over, but especially in the beginning of 1990's it was used by the leftist parties to block all attempts to cut the public welfare spending (Sundberg 1993, 420-421). This postponement rule was abolished from the Parliamentary Act from the beginning of September 1992. Because a postponement in a legislative proposal can be considered (at least a temporary) failure of government, this postponement rule has increased the possibilities of opposition parties affect legislation which has to be taken into consideration when calculating the voting power of parties.
The three different models or authority matrices as Knoke et al. (1996) call them are calculated as follows:
Legislative model:
This model is the simplest of the three models consisting of only one stage of decision making. The agenda setting power does not have a part in this model. The parties in the Parliament simply vote for law proposals and the voting power is calculated as the 'standard' Shapley-Shubik value for all parliamentary parties. Before the abolishment of the postponement rule a party is pivotal if 66 representatives (out of 200) vote 'yes' before it. After the abolishment of the postponement rule a party is pivotal if 100 'yes' votes are cast before it.
Policy Leadership model:
The Policy Leadership model takes the agenda setting power of the government into account. Now the voting power is calculated as a 'two-chamber' system, where the first chamber is the government voting and the second is voting in the Parliament. Before the abolishment of the postponement rule a party in the government is pivotal if more than 134 'yes' votes in the Parliament are cast and the party is pivotal in the government voting. A Parliament party is pivotal if more than half of the ministers in the government vote 'yes' and 66 'yes' votes are cast in the Parliament. After the abolishment of the postponement rule the situation is same except the number of 'yes' votes required in the Parliament are 100.
Party Government model:
The Party Government model is similar to the Policy Leadership model, except that the government parties decide to always vote as one group in the Parliament behind the government decision. In this situation it is possible to think that all government parties in the Parliament form one big party. Now the voting powers can be calculated same way as in the case of the Policy Leadership model. However, the voting power of the 'government' party must be somehow divided to individual agents. This is division is made in same proportion as the government parties have voting power in the government decision making stage.
The resulting voting power measures of these three models for each of the governments are shown in Table 8. Also the total power of government vs. opposition are shown. It is easy to see from the table that the voting power is most concentrated for the government parties in the Party Government model, and the opposition has biggest share of voting power in the Legislative model. Furthermore, shows that the abolishment of the postponement rule has increased the voting power share of the government. Especially, in the Party Government model the opposition is a total dummy player during Aho's government after the postponement rule was removed.