November 28, 2019

The story of the other wise mum

written by Manuel von Krosigk
The story of the other wise mum

…and how she used the subtle power of agenda setting

“What’s for dinner?” is a question that can be heard around the world on a daily basis, often asked after a hard day(‘s night) with urgency in anticipation of some delicious culinary delights. And yet, the issue of what’s for dinner is never more important than on big holiday gatherings like Thanksgiving or Christmas.

With large families and a variety of individual preferences, intolerances and (foodwise) incompatibilities, it can lead to many debates about what to prepare, serve and digest. In such situations, it is desirable to outsource such a delicate decision to an impartial, fair and democratic mechanism.

In order to provide an elegant solution to the “what’s for dinner” issue, let us consider the fictional van Dyke family and their Christmas dinner. Mrs. van Dyke is proficient in the art of Microeconomics and thus able to prepare a democratic poll. First, she determines the population of dinner alternatives, i.e. the family’s all-time favourites of Turkey, Goose, Fondue, Raclette and Lamb, based on previous years (for simplicity purposes, only the main course is considered. Starters, sides, desert as well as beverages derive naturally from the former). After validation of these choices she is then able to prepare a fitting ballot.

What the rest of the family don’t know is that Mrs. van Dyke has been paying close attention during the previous Christmas dinners, and is therefore well aware of each family member’s hidden preferences. In order to gain a sound overview, she lists what she considers to be the ranking for each participant:

Due to each family member’s status, it is clear that they prefer different dinner alternatives. For example, as Fondue is quite fiddly and poses some motoric challenges, the four grandparents – who are the most influential group in terms of quantity – prefer every other option which requires less attention. The children however, know how much fun Fondue can be to eat, using fondue sticks and lots of smaller ingredients, so it is their firm favourite. For the parents, who are responsible for cleaning up the resulting mess, this is not a preferred option – although it is slightly better than Turkey which the family eat all the time anyway.

From reading the TWS Blog, Mrs. van Dyke is aware of the importance of the voting system applied. She understands that the choice of voting system can have a significant impact on the outcome – a shocking revelation for watchers of the Eurovision Song Contest and participants in democratic voting systems.

Therefore, she lists a few popular voting procedures and considers which outcome they might yield for Christmas dinner

  1. Plurality voting: each family member has one vote and uses it for the alternative he/she ranks highest. In this case, the clear winner is Turkey.
  2. Plurality runoff: each family member has one vote and uses it for the alternative he/she ranks highest. If no alternative receives more than 50% of the votes, the vote is repeated with only the two alternatives with the most votes. In this case, the Turkey receives only 4 out of 9 possible votes and thus has to stand against Fondue in the second round, resulting in Fondue being chosen.
  3. Pairwise comparison with simple majority: each alternative is compared to exactly one other one, until only one alternative is left. In this case, Turkey is beaten by all other alternatives; Fondue is beaten by all alternatives except Turkey; Lamb is beaten by Goose and Raclette; Goose is beaten by Raclette. So Raclette wins the pairwise comparison with a simple majority.
  4. The Borda count: each family member awards 0 to 4 points to each alternative, according to their ranking. For example, the grandparents give 4 points to the Turkey, 3 to the Goose, 2 to the Lamb and so on. Afterwards, all points for each alternative are counted to determine the winner. In this case, Goose wins with 22 points (3 from the Grandparents, 2 from the children and parents, respectively).
  5. Approval voting: each family member can vote for as many alternatives as he/she prefers with equal weight, and the alternative with the most approval votes will be selected. In this case, it is possible that the children and parents go for their top two alternatives while the grandparents are ok with their first three, i.e. the proper traditional meat dishes of Turkey, Goose and Lamb. If that is the case, Lamb will be the winner since it is approved by the grandparents as well as the parents with 6 approvals in total, while Raclette receives 5 approvals, Turkey and Goose 4, and Fondue 3.

As we can see in this example, each of the five different voting procedures yields a different result. This is of no surprise to Mrs. van Dyke, who can use it to her advantage and determine the fate of Christmas Dinner without raising any suspicions. Aware of the responsibility and power that comes with being the agenda setter, she selects a voting method which ensures the joy and happiness of the whole family at the dinner table. After all, the family members appreciate the fair and transparent procedure under which their Christmas dinner was being determined – but which procedure did Mrs. van Dyke choose?

SOURCE:

Inspiration for this brief demonstration of agenda setting is taken from Nurmi, H. Soc Choice Welfare (1998) 15: 333. https://doi.org/10.1007/s003550050109 and has been widely discussed at various seminars of the author at the Stockholm School of Economics.