- #1

tom.stoer

Science Advisor

- 5,766

- 161

A couple of friends ##n = 1 \ldots N## of mine bet on the result of the next general election in Germany. We select the six most important political parties ##p = 1 \ldots 6##. For each party ##p## and each friend ##n## we have the forecast ##x_{pn}## and the official election result ##x_p##.

Now we calculate

$$D_n = \sum_p w(x_p) \, d(x_{pn} - x_p)$$

with a weight-function ##w## and a deviation-function ##d##. The winner is the guy with smallest ##D_p##.

My question is, what are the most reasonable functions?

It seems natural to set

$$d(x) = x^2$$

$$w(x) = 1$$

which corresponds to the Euclidean distance with equal weight for each party.

But of course other choices are conceivable, e.g.

$$w(x) = x^c$$

weighting bigger parties more than smaller parties.

Are there any reasonable arguments and choices for the weight-function ##w## and the deviation-function ##d##?

Now we calculate

$$D_n = \sum_p w(x_p) \, d(x_{pn} - x_p)$$

with a weight-function ##w## and a deviation-function ##d##. The winner is the guy with smallest ##D_p##.

My question is, what are the most reasonable functions?

It seems natural to set

$$d(x) = x^2$$

$$w(x) = 1$$

which corresponds to the Euclidean distance with equal weight for each party.

But of course other choices are conceivable, e.g.

$$w(x) = x^c$$

weighting bigger parties more than smaller parties.

Are there any reasonable arguments and choices for the weight-function ##w## and the deviation-function ##d##?

Last edited: