On June 15-16 2017 HHL hosted the 4th Workshop on Cooperative Game Theory in Business Practice. I gave a presentation on the conditional Shapley value (joint work with Andre’ Casajus), starting around 27:00 in the video below.
Next year there will be many exciting elections around the world that we would like to follow. Here is a list of upcoming parliamentary elections in 2019, taken from Wikipedia:
- European Union, Parliament
- Moldova, Parliament
- Thailand, Parliament
- Estonia, Parliament
- Finland, Parliament
- Belgium, Federal
- Denmark, Parliament
- Botswana, Parliament
- Canada, House of Commons
- Greece, Parliament
- Switzerland, Federal Assembly
- Tunisia, Parliament
- Poland, Parliament
- Australia, House of Representatives
- Dominica, Parliament
- India, Parliament
- Israel, Parliament
- Solomon Islands, Parliament
- South Africa, Parliament
The projections below are obtained using current poll data taken from INSA/YouGov. Based on poll data, we predict:
- the number of seats for each party (above the 5% cut-off)
- all minimal winning coalitions
- all stable coalitions (according to the conditional Shapley value: see http://)
- for each stable coalition, the proportion of ministries received by all member parties.
The first column of output data after the party names shows the predicted fraction of the total vote according to current poll data. The second column shows the predicted number of seats to each party, while the third column shows how much strategic “strength” (measured by the Shapley value, and interpreted as fraction of the total weighted number of available ministry positions) each party expects before any coalition talks, disregarding ideological propensity or aversion towards other potential coalition partners.
The remaining lines of output list all minimal winning coalitions, and all coalitions which are stable with respect to the conditional Shapley value. One can see from the output that there are 11 minimal winning coalitions, in that in each such coalition all members are needed in order to achieve a majority. Out of those 11 minimal winning coalitions there are four which in addition are also stable with respect to the conditional Shapley value. That means that, if all parties formulate their expectations according the conditional Shapley value, then there are no expected profitable deviations which could lead the members of a different winning coalition to assemble together. (One normally speaks about stable coalition structures, but in majority games we can simply denote a stable structure by its minimal winning coalition.)
Yet, the four stable coalitions (BCDE, BCDF, BCEF, and BDEF) are all unrealistic in that they would involve parties that are ideologically very different, and moreover would violate explicit campaign promises. If we exclude all those coalitions forbidden by official party policy, namely, all those including F, and all those including both D and E, then the resulting stable coalitions (according to the conditional Shapley value) are ACD (“Jamaica”), and ACE.
The predicted proportion of ministries for a party in a given coalition is given by the Shapley value times the stability coefficient. Hence, if coalition AB forms, party B would receive 20% of (60/49), which is just below 25% of the ministry positions, while A would receive the remaining 75%. By contrast, if coalition ACD forms party A would receive 61.67% of (30/23), which is around 80% of ministry positions; party C would receive 11.67% times the same coefficient, which is about 15% of ministries; and party D would receive the remaining 5%.Comparing the current scenario with the situation after the 2013 election, the results can be summarized as follows. Let us stipulate that a Chancellor position is roughly worth five ministries, so that a total of 20 ministerial positions must be assigned to coalition partners.In 2013, in the absence of the FDP as a potential coalition partner, the CDU/CSU conceded six ministries (about one third of the total) to the SPD in order to form the ‘Grand Coalition’ AB. Today, based on current poll data the SPD would still expect to receive five ministries (25% of the total) in order to form a Grand Coalition with the CDU/CSU. But now that the FDP is once again above the 5% cut-off, and hence available as a coalition partner, the CDU/CSU can also form coalition ACD by offering three ministries to the Green (15% of the total) and one to the FDP (5% of the total).
Note that, despite the existence of a winning coalition BCE, in which the SPD would have expected one third of the ministerial positions, the SPD decided to accept the same one-third share in a Grand Coalition with the CDU/CSU. This suggests that the decision of the SPD was also motivated by a desire to second, rather than counteract, the large shift of votes to the right that the 2013 election had brought up by positioning itself as member of a centrist, rather than left-wing, coalition. From its side, the CDU/CSU preferred to offer one extra ministry (six rather than five) to the SPD in order to make the AB coalition stable, and hence remove any potential threat of being excluded from the government in case the BCE coalition would form.