J.-E. LANE, A. M. PREKER
Below political parties will be looked upon as organised
players making coalitions involving a perfect degree of indi-
vidual party member discipline.
Ex Ante and ex Pos t Voting Power
The representative assembly makes a huge number of deci-
sions concerning for instance government formation and sup-
port, the budget and taxation as well as regulation in the form
of legislation and policies. Additional functions of parliament
include controlling government and articulating relevant prob-
lems as well as electing government. Under party government,
the actors in collective decisions are the political parties that
tend to vote with one voice, based on their differential number
of mandates. Both the constitutional rules of decision-making
and the strategy of coalition formation are decisive for the out-
comes of parliamentary decision-making.
Most decisions in Parliament require simple majorities,
which is why a minimum winning coalition is enough. Some-
times certain decisions of constitutional relevance are singled
out requiring a heavier support or qualified majority. To prevail,
a winning coalition would then have to be oversized. In the
normal business of government, simple majority suffices in
most parliamentary countries.
A coalition that is minimum winning does not need to be a
minimum sized coalition. Actually, coalitions may be of many
kinds, but the essential thing is that they win the voting se-
quences. Coalitions may be temporary, focusing on one voting
sequence, or they may be permanent over an election period,
such as for instance 4 years. Government coalitions are formed
for the purpose of exercising power over a longer period, but
government coalitions may break up prematurely, leading either
to a new government or to new elections.
A political party maximizes its voting power by actively par-
ticipating in the formation of coalitions. If it enters a govern-
ment coalition, then it shares the voting power of the govern-
ment with its governing partners. It may also exercise voting
power by participating in temporary coalitions that achieve the
minimum-winning format. Political power is mainly exercised
through the capacity to influence voting in the national assem-
bly. Typical for continental European democracies is the multi-
party system, meaning that the parliamentary arena is com-
prised of three or more political parties, where no party has a
majority position.
One may enquire after the differences in seats and voting
power for the major political parties under the regime of party
government by calculating two power index scores: ex ante
power measures based upon the election outcomes before gov-
ernment formation, and ex post power measures based upon the
pattern of government formation: minority, simple majority,
oversized, etc., after government formation. The following dis-
tinctions can be made in this new method for the calculation the
power of parties under party government:
a) The calculation of ex ante power scores is the straightfor-
ward solution of the Banzhaf game for parties in the legislature
before the formation of a government or government coalition.
b) The calculation of the ex post power scores involves a
double Banzhaf game for the parties after government forma-
tion, where the parties in a government coalition share whatever
power government has in the legislature, on the basis of a una-
nimity game between the government coalition partners.
One may in principle distinguish between two parliamentary
situations: a majority coalition and a minority coalition. The
voting power score of the government coalition will here be
assumed to be equally shared among the coalition parties on the
basis of an imagined second Banzhaf game within the govern-
ment—a unanimity game among equal coalition partners. Thus,
we have:
1) Banzhaf number or score for a simple majority govern-
ment = the party(ies) in government constitute the winning
coalition in legislative voting (Banzhaf score = 1/number of
parties in the government coalition).
2) Banzhaf number or score for a minority government = the
party(ies) in government enter some of the winning coalitions
in the legislature (Banzhaf score 0 < 1/number of coalition par-
ties). When the coalition government does not control the vot-
ing in the legislature, it is forced to make ad hoc coalitions with
the other parties—see Appendix for an example.
When there is a minority coalition government, other parlia-
mentary actors like the opposition parties will receive Banzhaf
scores as well, depending on whether they are decisive in coali-
tions.
c) One may further calculate the parties’ Banzhaf power in-
dex numbers for both minority and majority coalitions for every
legislative period and weighted for every single year, thus ar-
riving at aggregated scores for legislative periods, and longer
time spans.
d) By relating the ex post Banzhaf scores to the relative size
of the parties’ representation in the legislative assembly (seats
or mandates), it can be shown how the parties’ voting power
differ from their sizes in Parliament, because some parties tend
to dominate the political game, whereas others do not play a big
role despite their relative strength.
Let us proceed to a couple of examples from the spectacular
political history of democracy in Germany and Austria.
Example: Party Government in the Two
German Speaking Nations
Germany
Proportional election formulas have been utilized in Ger-
many to establish a legislative assembly. In compliance with
parliamentarism, main power lies with the Kanzler. Two kinds
of governments prevail: simple majority governments (FRG)
and minority governments/coalitions (Weimar). There have
only been a few consociational governments. In the Weimar
Republic, the disproportion between the size of representation
of the left-wing (seats, mandates) and its ex post Banzhaf vot-
ing power is striking. In the FRG, an effort was made to elimi-
nate this effect, but has it been successful?
The Weimar Republic
In the Weimar Republic the smaller and right wing parties
often augmented their voting power in comparison to their
share of seats in the Reic hstag by joining government. This
discrepancy and disproportionality can be demonstrated by
subtracting the parties’ relative share of seats from its ex post
Banzhaf points: Especially DDP and BVP enlarged their influ-
ence and voting power in comparison to their share of seats
(DDP + 6.7 per cent, BVP + 5.3 per cent). But also larger con-
servative parties, that is Zentrum and DVP, increased their vot-
ing power by entering the mainly minority governments. Ap-
parently, party coalitions, first minority governments, then
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