Cofounder of Beeminder
Really good points. It's funny, I have a draft of a similar point about personal behavior change that I tried to make as provocative-sounding as possible:
http://doc.dreev.es/carbonfoot (Trying To Limit Your Personal Carbon Footprint Hurts The Environment)
But note the PS where I suggest a counterargument: making personal sacrifices for climate change may shape your identity, drive you to greater activism, and make your activism and climate evangelism more persuasive (to those who don't appreciate the economics and game theory of it).
Nice! I've heard a similar idea called a "talent stack" or "skill stack" but explaining it in terms of staking out a chunk of the Pareto frontier is much better.
Coincidentally, I just wrote a post explaining the idea of Pareto dominance -- http://blog.beeminder.com/pareto -- in case that's useful to anyone.
Thank you! See above ("Better to not have people feel like their desperation is being capitalized on.") for my response to your first question. And we actually believe that our system is, in practice if not in theory, strategy-proof. It's explicitly ok to game the system to our hearts' delight. It seems to be quite robust to that. Our utilities tend to either be uncannily well-matched, in which case it's kind of a coin flip who wins, or they're wildly different, but we never seem to have enough certainty about how different they'll be for it to be fruitful to distort our bids much.
The strategy of "just say a number such that you're torn about whether you'd rather win or lose" seems to be close enough to optimal.
How about adding a tiny bit of ambiguity (or evasion of the direct question) and making up for it with more effusiveness, eg, "it's not only my job but it feels really good to know that I'm helping you so I really want you to bug me about even trivial-seeming things!" All true and all she's omitting is her immediate annoyance but that is truly secondary, as she points out below about first-order vs second-order desires.
Yes, we're super keen to make sure the efficient thing happens regardless of the initial distribution of resources/responsibilities/property-rights/etc. And we use yootling as a bargaining mechanism to make that happen. In general we're always willing to shove work to each other or redistribute resources as efficiency dictates, using payments to make that always be fair.
In practice the sealed-bid version seems to be ungameable, at least for us! None of the problems you mentioned have arisen. My parents have tried this and had more problems but as far as I could tell it always involved contention about what to consider to be joint 50/50 decisions. Bethany and I seem to have no problem with that, using the heuristic of "when in doubt, just call it a 50/50 decision and yootle for it".
Fixed and fixed. Thank you!
I'm impressed! That's kind of the conclusion we gradually came to as well, after a lot of trial and error. Better to not have people feel like their desperation is being capitalized on.
Another way to put it: when you're really desperate to win a particular auction it's really nice to be able to just say so honestly, with a crazy high bid. Trying to allocate the surplus equitably means that I have to carefully strategize on understating my desperation. (And worst of all, a mistake means a highly inefficient outcome!)
PS: To be clear about first-price vs second-price, it's technically neither since there's no distinct seller.
Here's the n-player, arbitrary shares version:
Each participant starts with some share of the decision.
Everyone submits a sealed bid, the second-highest of which is taken to be the Fair Market Price (FMP).
The high bidder wins, and buys out everyone else's shares, ie, pays them the appropriate fraction of the FMP.
"Even yootling", or just "yootling", refers to the special case of two players and 50/50 shares.
In that case, instead of bidding a fair market price (FMP), you say how much you're willing to pay if you win.
True FMP is twice that, since you only have to pay half of FMP with even yootling.
So instead of deciding what you'd pay, doubling it to get FMP, then halving FMP to get the actual payment, we short circuit that and you just say the payment as your bid.
For yootling with uneven shares it's easier to bid FMP and then pay the appropriate fraction of that.
Bethany and I philosophically bite the bullet on this, which is basically to just agree with your second point: the wealthy person gets their way all the time and the poor person gets what's to them a lot of money and everyone is happy.
If that's unpalatable or feels unfair then I think the principled solution is for the wealthy person to simply redress the unfairness with a lump sum payment to redistribute the wealth.
I don't think it's reasonable -- ignoring all the psychology and social intricacies, as I'm wont to do  -- to object both to auctions with disparate wealth and to lump sum redistribution to achieve fairness.
Now that I'm introspecting, I suppose it's the case that Bethany and I tend to seize excuses to redistribute wealth, but they have to be plausible ones.