Would one only use ‘direct steps’ in decision-making? How is “path dependency” interpreted?
I’m not sure what you are referring to here. I would flag that the relative value type specification is very narrow—it just states how valuable things are, not the “path of impact” or anything like that.
After talking to GPT about this[1], I think that my concern is actually already covered by your
If people were doing it by hand, there could be contradictory properties, as you mention. But with programming, which we likely want anyway, it’s often trivial or straightforward to make consistent tables.
and could be addressed to a large degree with a few automatized checks and a user interface (one could even auto-fill the table given the first line of entries by assuming ~maximum resulting uncertainty for the unknown correlations). I feel like this could be really helpful for reflecting on one’s values if done right, or overwhelming if done wrong.
[GPTs answer includes a summary, so I’ll leave out my prompt:] I see your point now. You’re referring to a potential inconsistency in the triangle inequality context for relative values. Let’s use a concrete example to explore this.
Suppose the relative value of ‘chocolate’ to ‘vanilla’ is given by a 90% credibility interval from 0.8 to 1.2, and ‘banana’ to ‘vanilla’ is from 1.0 to 1.5. This would imply that, based on your preferences for chocolate and banana ice cream relative to vanilla, ‘banana’ should have a relative value compared to ‘chocolate’ that lies within a certain range.
If, however, you then provide a wide 90% credibility interval for ‘chocolate’ to ‘banana’ (e.g., 0.2 to 5), it may seem inconsistent with the narrower ranges implied by the comparisons with ‘vanilla’.
In this case, it may be that you need to revisit your estimates for ‘chocolate’ to ‘vanilla’ and ‘banana’ to ‘vanilla’. If you feel a lot of uncertainty about ‘chocolate’ vs. ‘banana’, perhaps you also should feel more uncertainty about these options compared to ‘vanilla’ than you initially thought. You may have overestimated your confidence in these comparisons.
Alternatively, if you’re confident in your estimates of ‘chocolate’ to ‘vanilla’ and ‘banana’ to ‘vanilla’, you may want to narrow down your 90% credibility interval for ‘chocolate’ vs. ‘banana’.
In any case, it’s a good point to keep in mind when building a relative value table. You want to be consistent in your uncertainty estimates across different comparisons. If there seems to be a contradiction, it’s a sign that you may need to rethink some of your estimates.
After talking to GPT about this[1], I think that my concern is actually already covered by your
and could be addressed to a large degree with a few automatized checks and a user interface (one could even auto-fill the table given the first line of entries by assuming ~maximum resulting uncertainty for the unknown correlations). I feel like this could be really helpful for reflecting on one’s values if done right, or overwhelming if done wrong.
[GPTs answer includes a summary, so I’ll leave out my prompt:] I see your point now. You’re referring to a potential inconsistency in the triangle inequality context for relative values. Let’s use a concrete example to explore this. Suppose the relative value of ‘chocolate’ to ‘vanilla’ is given by a 90% credibility interval from 0.8 to 1.2, and ‘banana’ to ‘vanilla’ is from 1.0 to 1.5. This would imply that, based on your preferences for chocolate and banana ice cream relative to vanilla, ‘banana’ should have a relative value compared to ‘chocolate’ that lies within a certain range. If, however, you then provide a wide 90% credibility interval for ‘chocolate’ to ‘banana’ (e.g., 0.2 to 5), it may seem inconsistent with the narrower ranges implied by the comparisons with ‘vanilla’. In this case, it may be that you need to revisit your estimates for ‘chocolate’ to ‘vanilla’ and ‘banana’ to ‘vanilla’. If you feel a lot of uncertainty about ‘chocolate’ vs. ‘banana’, perhaps you also should feel more uncertainty about these options compared to ‘vanilla’ than you initially thought. You may have overestimated your confidence in these comparisons. Alternatively, if you’re confident in your estimates of ‘chocolate’ to ‘vanilla’ and ‘banana’ to ‘vanilla’, you may want to narrow down your 90% credibility interval for ‘chocolate’ vs. ‘banana’. In any case, it’s a good point to keep in mind when building a relative value table. You want to be consistent in your uncertainty estimates across different comparisons. If there seems to be a contradiction, it’s a sign that you may need to rethink some of your estimates.