Cost of Fairness: Splitting Vehicle Hire Costs

[whiskeredbat]

My partner and I hired a vehicle for a holiday - due to travel circumstances I enjoyed 10/10 days of the hire and my partner (who joined later) had 7/10 days. We later had to split the cost of the hire and insurance. I believed the fairest cost to be for me to stump up 10/17ths of the hire (=59%) and my partner to stump up 7/17ths (=41%). "No" she said - "you had 3 whole days and 7 half days (= 6.5/10 = 65%) and I had 7 half days (= 3.5/10 = 35%). Ergo My proportion would be 59% or 65% and my partners would be 41% or 35%; depending upon the definition of 'fairness'.
Which, if either, belief, is the fairer as a mathematical solution, and why?
Grateful for help, although we compromised on 62% and 38%.

 

[I like Serena]

Hi whiskeredbat, welcome to MHB!

I guess this is not really a mathematical question, but more of an ethical or moral question.
Anyway, let's see...

As I see it, there are 2 scenarios:

1. It was agreed and expected to use the vehicle 10 days together with the corresponding expectations on costs.
   If one party unexpectedly drops out (partially), it does not seem fair that the remaining party suddenly has to bear the unexpected extra costs.
2. It was agreed and expected to use the vehicle shared when actually sharing, and otherwise any costs were out of scope.
   If this was agreed beforehand, then there is no problem.

Ideally the scenario was clarified beforehand, but presumably that was not the case.
Ultimately it boils down on expectations that may or may not have been fully clarified beforehand.
Problems (disappointments) generally stem from expectations that were not realized, which then have to be resolved in some fashion that is acceptable to both parties.
The usual solution is a compromise that effectively makes both parties equally unhappy, but something that they can both accept, forget about, and move on. That is as opposed to a solution that is perceived by at least one party as unfair, and that keeps haunting both of you for a long time to come.

In scenario 1 it is now unclear what the case is for the days only 1 party had the use of the vehicle.
Was that fully beneficial as that party fully enjoyed the use of the vehicle without sharing?
In that case a 3+7/2 : 7/2 ratio is fair, which amounts to 13/20 (65%) of the costs versus 7/20 (35%).
Or was that actually counter-beneficial as the expected 'fun' or 'use' from sharing a journey was not realized?
In that case those 3 days could be seen as 'lost'. Assuming we don't ask for 'damage compensation', a 7/2 : 7/2 ratio would then be fair - just for the days actually spent together while using the vehicle. This is also the cost division as it was expected to be beforehand (50% versus 50%).

From the perspective of an equally-unhappy-compromise we might pick a 50-50 solution.
Either way, the 'sweet' spot should be somewhere in between the best-case and worst-case scenarios, which is open for discussion and depends on how the benefits are perceived. Ultimately the goal is to achieve a division that both parties are more or less equally happy with, so that both can move on with happy rather than bad memories.

TL;DR: Ideally you establish for both parties what the perceived benefits are - and then split the difference.
And if one of the parties feels 'cheated', perhaps renegotiation is in order to reestablish those perceived benefits and subsequently achieve the proper split of costs, and more importantly, be able to move on without haunting regrets.

 

[whiskeredbat]

Hi whiskeredbat, welcome to MHB!

I guess this is not really a mathematical question, but more of an ethical or moral question.
Anyway, let's see...

As I see it, there are 2 scenarios:

1. It was agreed and expected to use the vehicle 10 days together with the corresponding expectations on costs.
   If one party unexpectedly drops out (partially), it does not seem fair that the remaining party suddenly has to bear the unexpected extra costs.
2. It was agreed and expected to use the vehicle shared when actually sharing, and otherwise any costs were out of scope.
   If this was agreed beforehand, then there is no problem.

Ideally the scenario was clarified beforehand, but presumably that was not the case.
Ultimately it boils down on expectations that may or may not have been fully clarified beforehand.
Problems (disappointments) generally stem from expectations that were not realized, which then have to be resolved in some fashion that is acceptable to both parties.
The usual solution is a compromise that effectively makes both parties equally unhappy, but something that they can both accept, forget about, and move on. That is as opposed to a solution that is perceived by at least one party as unfair, and that keeps haunting both of you for a long time to come.

In scenario 1 it is now unclear what the case is for the days only 1 party had the use of the vehicle.
Was that fully beneficial as that party fully enjoyed the use of the vehicle without sharing?
In that case a 3+7/2 : 7/2 ratio is fair, which amounts to 13/20 (65%) of the costs versus 7/20 (35%).
Or was that actually counter-beneficial as the expected 'fun' or 'use' from sharing a journey was not realized?
In that case those 3 days could be seen as 'lost'. Assuming we don't ask for 'damage compensation', a 7/2 : 7/2 ratio would then be fair - just for the days actually spent together while using the vehicle. This is also the cost division as it was expected to be beforehand (50% versus 50%).

From the perspective of an equally-unhappy-compromise we might pick a 50-50 solution.
Either way, the 'sweet' spot should be somewhere in between the best-case and worst-case scenarios, which is open for discussion and depends on how the benefits are perceived. Ultimately the goal is to achieve a division that both parties are more or less equally happy with, so that both can move on with happy rather than bad memories.

TL;DR: Ideally you establish for both parties what the perceived benefits are - and then split the difference.
And if one of the parties feels 'cheated', perhaps renegotiation is in order to reestablish those perceived benefits and subsequently achieve the proper split of costs, and more importantly, be able to move on without haunting regrets.

Klaas - Thank you very much for responding