This is an underappreciated fact! I like how simple the rule is when framed in terms of size and distance.
You mention both the linear and log rules. The log rule has the benefit of being scale-invariant, so your score isn't affect by the units the answer is measured in, but it can't deal with negatives and gets overly sensitive around zero. The linear rule doesn't blow up around zero, is shift-invariant, and can handle negative values fine. The best generic scoring rule would have all these properties.
Turns out (based on Lambert and Shoham, ... (read more),,,,,,,,,,,,,,,,,,,,
This is an underappreciated fact! I like how simple the rule is when framed in terms of size and distance.
You mention both the linear and log rules. The log rule has the benefit of being scale-invariant, so your score isn't affect by the units the answer is measured in, but it can't deal with negatives and gets overly sensitive around zero. The linear rule doesn't blow up around zero, is shift-invariant, and can handle negative values fine. The best generic scoring rule would have all these properties.
Turns out (based on Lambert and Shoham, ... (read more),,,,,,,,,,,,,,,,,,,,