Optimal Allocation with Noisy Inspection

How do you inspect and select an option when you know the option is informed, and cares about ultimately being selected? πŸ€”

This is a short (plain-English) post about a paper I have in economic theory and mechanism design. 🚨

Inspecting options in order to assess their value is a very common activity; employers interview potential employees, public funds assess grant applications, venture capitalists evaluate investment opportunities. πŸ’Ή

My paper, "Optimal Allocation with Noisy Inspection", examines how we should design an inspection and selection rule in order to gather information and make the best selection. 🍎

Here, the option could be a person we might like to hire for a job, an applicant we might like to grant the use of our facilities to, or a start-up we might like to invest in. Inspection is then an interview, assessment or evaluation of the option which tells us more about it but will cost us our time, money and effort; things we can't get back! πŸ’Έ

When information is noisy - it doesn't tell us whether the option is good or bad for sure - and privately held - the option is the one with the relevant information - costly efforts to gather this information involve both verification and discovery. πŸ”

This means that we will have to over-select bad options, over-inspect good options, and reject some options that are revealed as worthy of selection! This is the main result of the paper. ⭐

We have to select some bad options because, even though we don't want to accept them, they need an incentive to tell us that they are indeed bad options, rather than lie and say that they are good. For the good options, even though we'd like to accept them without bothering with an inspection, we must inspect them in order to make sure that they aren't bad ones in disguise. πŸ‘»Β 

But we can do better! If we throw away some slightly good options, we can further protect ourselves from the bad options claiming they are good by reducing their incentives to lie, and this allows us to reject more bad options in the first place. While the selection will not always ideal, this rule allows us to gather more initial information, and on average we will make a better selection overall. βœ…

The existing literature is silent on the discovery aspect of inspection, instead focusing on verification or "screening". In these papers, it is assumed that the option has perfect information - they know for sure whether they are good or bad. I think a great deal can be done in exploring settings where information is noisy. πŸ”¦

For example, how should we allocate natural resources when the user doesn't know exactly how costly their use will be? How should we decide on which articles to publish when the truth of the article is unknown? How should we allow a court of law to collect and judge evidence when this evidence only tells us part of the story? πŸ‘©β€βš–οΈ

My paper also provides explicit comparative statics - how the results change when you change the assumptions. This opens the door to studying how these inspection and selection rules work in the real world and what assumptions are "right", an exercise that is called empirical analysis. πŸ‘€

The primary motivation for this paper is to outline the best way to use inspection and to show what this looks like. For the Australians out there: I just want inspection that tastes like real inspection, and this tastes like real inspection, and only 2% fat!Β  For non-Aussies, see the reference below.πŸ₯›

You can read the full paper here. ✌️