The political scientists Hans Daudt and Douglas W. Rae presented an election paradox in 1976, the Ostrogorski Paradox (on) , named after the Russian party researcher Moissei Ostrogorski . The paradox shows that there can be strong distortions of the “will of the electorate” in elections and votes if votes are taken on complete party programs and not (separately) on individual issues.

The social choice theory examines and compares u. a. different aggregation methods and their problems and advantages.

## example

Suppose there are two parties, three issues on which the parties have different ideas, and four groups of voters.

• Voting group A, which makes up 20%, prefers party X for topic 1, party Y for topic 2 and party Y for topic 3.
• Voting group B, which also accounts for 20%, prefers party Y for topic 1, party X for topic 2 and party Y for topic 3.
• Voting group C, which also accounts for 20%, prefers party Y for topic 1, party Y for topic 2 and party X for topic 3.
• Finally, voter group D, which accounts for 40%, prefers party X for topic 1, party X for topic 2 and also party X for topic 3.

If you were to count according to topic groups, the result would be as follows:

• For topic group 1, party X would have won (A 20% + D 40%) 60%.
• For topic group 2, party X would also have won 60% with (B 20% + D 40%).
• For topic group 3 too, party X would have won 60% with (C 20% + D 40%).

If one does not count separately according to topics and assume that every topic is equally important to each group of voters, paradoxically one arrives at a different result:

• Voter groups A, B and C (one X, two Y), together 60%, prefer party Y.
• Voter group D (three times X), 40%, prefers party X.

In this case, party Y would have won with (A 20% + B 20% + C 20% =) 60%.

Voter group proportion of Party preference on topics Majority by group Total election result by group Satisfaction with
Topic 1 Topic 2 Topic 3 Party X Party Y
Voting group A 20% X Y Y 0.2 x Y Party Y wins with 60% of the vote 33.3% 66.7%
Voter group B 20% Y X Y 0.2 x Y 33.3% 66.7%
Voter group C 20% Y Y X 0.2 x Y 33.3% 66.7%
Voter group D 40% X X X 0.4 x X 100% 0%
Majority by subject 0.6 X 0.6 X 0.6 X Majority after satisfaction 60% 40%
Overall election result by topic Party X wins with 60% of the vote Overall election result according to satisfaction Party X wins with 60% of the vote

Let the satisfaction of a group of voters with a party, expressed in percent, be as great as this party agrees with the group of voters in terms of the number of topics.

The overall satisfaction in the above sense is distributed like the approval by topic. However, if each voter chooses the party they are more inclined to (according to the number of thematic matches), party Y is chosen instead of party X and the overall satisfaction is 40% instead of 60%.

If one assumes that voters behave perfectly sensible, i.e. as homo oeconomicus , as a party one does not have to convince 51% of the voters 100% of themselves. It is enough to communicate thematically with 51% of voters 51% agreement to get to power. Even a 100% dissonance with the remaining 49% of voters in the extreme case would not change anything. In this extreme case, the overall satisfaction defined above would be just 26.01%.