You and your spouse plan your lifetime household consumption collectively. This is complicated because you have different discount factors. Your wife is patient, her discount factor is .8; you are not so patient, your discount factor is .5. But you are a utilitarian household so you resolve your conflicts by maximizing the total household utility.
Leeat Yariv and Matt Jackson show in this cool paper that your household necessarily violates a basic postulate of rationality: your household preferences are not time consistent. For example, consider how you rank the following two streams of household consumption:
- (0,10,0,0, …)
- (0,0,15,0,0, …)
Each of you evaluates the first plan by computing the present value of 10 units of consumption one period from now. Total household utility for the first plan is the sum of your two utilities, i.e. 
But now consider what happens when you actually reach date 1 and you re-consider your plan. Now the total utilities are 
Indeed your household exhibits a present bias: present consumption looms large in your household preferences, so much so that you cannot forego consumption that, earlier on, you were planning to delay in exchange for a greater later reward.
Jackson and Yariv show that this example is perfectly general. If a group of individuals is trying to aggregate their conflicting time preferences, and if that group insists on a rule that respects unanimous preferences and is not dictatorial, then it must be time inconsistent.
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October 12, 2011 at 11:15 pm
db
Congress explained at last
October 12, 2011 at 11:50 pm
Nageeb Ali
Here’s a newer version with an experiment too:
Click to access collectiveTime.pdf
October 13, 2011 at 2:43 am
Lones Smith
Simple and sweet idea. It does micro theory proud.
October 13, 2011 at 12:57 pm
Daniel Gottlieb
This is a related paper where each member of the household has imperfectly aligned altruism (I care about my consumption slightly more than my partner cares about my consumption). The equilibrium is also time-inconsistent and exhibits a present bias:
Click to access HH_Paper_July_15_2011.pdf
October 15, 2011 at 4:09 am
Décisions collectives et incohérence intertemporelle « Rationalité Limitée
[…] Jeff Ely sur Cheap Talk rapporte les résultats d’un papier de Matthew Jackson et Leeat Yariv sur le lien entre décision collective et incohérence intertemporelle. Jackson et Yariv montre qu’à partir du moment où les membres d’un groupe ont des préférences temporelles (mesurées par un facteur d’actualisation) conflictuelles et que ce groupe agrège les préférences des individus par une procédure non dictatoriale, alors les décisions du groupe manifesteront une incohérence intertemporelle, c’est à dire une inversion des préférences dans le temps. Share this:TwitterFacebookPrint"Aimer" ceci :"J'aime"Soyez le premier à aimer ce post. […]
October 15, 2011 at 9:38 pm
some name
I like this kind of result. But I can’t help but wonder how “cool” this paper would be if it were written by a no-name. (This is not a comment to disparage Yariv nor Jackson.)
October 19, 2011 at 1:23 pm
Kabir
In the example above if the sum of the discount rates is less than one then the preferences dont flip once the second period approaches. I havent read the paper (yet) but the above example at least is not completely general right?
October 19, 2011 at 2:05 pm
K
Actually, my last comment is not quite right. The flip in the above simple example would happen as long as the ratio of the payoffs is with the range determined by the discount factor, i.e (d1+d2)/2 and (d1^2+d2^2)/(d1+d2). Now off to read the paper to see what the authors do…