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Gordon Seidoh Worley Sep 13, 2021, 6:27 PM
4 points
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I didn’t quite follow. What’s the reasoning for claiming this?
From the definition of the four variables, the following equivalence can be deduced:
$w - y = x - z ⟺ w - x = y - z$
- Benedikt Schmidt Sep 15, 2021, 10:53 AM
  2 points
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  Parent
  The reasoning is the following:
  The agent-neutral values are now denoted by variables instead of numbers.
  The worst case is represented by $z$ , where the agent neither enjoys the beneﬁts
  of PAP, nor those of RXR. $y$ represents the value yielded by the choice of
  PAP whereas $x$ corresponds to the value yielded by the choice of RXR. The
  best case arises if the agent chooses PAP while RXR is not necessary, since
  then the agent-neutral value incorporates the beneﬁts of PAP and RXR,
  amounting to $w$ . Therefore, clearly the following relation holds:
  $w > x > y > z$
  From there, the equivalence under question follows.
  Do you agree?
  - Gordon Seidoh Worley Sep 16, 2021, 3:58 PM
    2 points
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    Parent
    I guess I don’t understand why w > x > y > z implies w—y = x—y iff w—x = y—z. Sorry if this is a standard result I’ve forgotten, but at first glance it’s not totally obvious to me.
    - Benedikt Schmidt Sep 16, 2021, 4:30 PM
      1 point
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      Parent
      Maybe it gets clearer if you compare the relative values of the 4 variables. $w - y$ corresponds to the benfits of RXR, $x - z$ also corresponds to the benefits of RXR. But maybe I was not precise enough: The equivalence does not follow only from $w > x > y > z$ , we also need to take into account the definitions of the 4 variables.
      Do you see what I mean?
Venky1024 Sep 14, 2021, 12:08 PM
1 point
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I didn’t get the intuition behind the initial formulation:
$E U (f) = α {min}_{p \in C} E_{p} U (f) + (1 - α) {max}_{p \in C} E_{p} U (f)$
What exactly is that supposed to represent? And what was the basis for assigning numbers to the contingency matrix in the two example cases you’ve considered?
- Benedikt Schmidt Sep 15, 2021, 10:50 AM
  3 points
  0 ∶ 0
  Parent
  Thanks for your question!
  This is how the $α$ -maxmin model is defined. You can consider the coefficient $α$ as a sort of pessimism index. For details, see the source Ghirardato et al.
  It is supposed to represent the extreme cases.
  The numbers in the examples are exemplary. The purpose is to have two different cases in order to study.