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Food hygiene ratings and the full disclosure principle

In 2013 a system was introduced in Wales where restaurants and food outlets were required to display food hygiene ratings for all to see. This has seemingly led to an increase in food hygiene, prompting calls for the system to be extended across the UK. But is it necessary to force restaurants to display the rating? Textbook models of signalling would suggest not. Here's why:
          Restaurants are rated on a 6 point scale ranging from a cockroach infested 0 to very good 5. All restaurants have to be rated and so this is not at issue. The question is whether they should be forced to prominently display the rating. With that in mind, consider the incentives of restaurant owners:
        It is easiest to start with a restaurant that got a top, 5 rating. Clearly the owners have an incentive to display the high rating and show off how good the are. So they will likely display the rating whether forced to or not.  
        What about a restaurant with a 4 rating? You might think the owners would not want to display the rating as this will signal that they did not get a 5 rating. Suppose, however, the owners do not display the rating? The customer can reason that if the restaurant had got a 5 rating they would surely have displayed it. The lack of rating should, therefore, be interpreted as a signal the restaurant did not get a 5. And, who knows, it might have got a 0. It is, therefore, in the interests of the owners to display their 4 rating - it is not a 5 but it is better than a 3, or 0.
         What about a restaurant with a 3 rating? These owners would surely rather hide the fact they only got a 3. Again, however, we need to consider what the absence of a rating would signal. If all restaurants with a 5 or 4 display their ratings then the absence of a rating is a signal of 3 or below. And it is better to admit a 3 than have customers infer the rating might have been 2, or 0.
         This full-discloure principle extends to those with a 2 and 1 rating. The only restaurants that have no incentive to display their ratings are those with a 0. And we would hope that those are shut down anyway.
         Naturally, we might question whether reality would match the prediction of voluntary disclosure. But, I think there is a lot of anecdotal evidence to suggest it will. Indeed, the success or rating sites like TripAdvisor would seem to be dependent on it. Suppose, for instance, that only the best hotels, restaurants etc. wanted to be featured on rating websites. Then the website would have so few rankings as to be essentially useless. Things work because it is in the interests of all (or just about all) hotels and restaurants to let people know their rating. A rating of 7.5 out of 10, for example, is not great but better the customer know this than think the rating is 6.5 or worse.

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