Interesting question regarding whether Groupon increases or decreases societal welfare. IMO Groupon is an 'excess inventory' business. They find places which have tables, food, drinks, spots free and sell them at deeps discounts to attract customers to fill those spots. So I do not think that is a net increase in welfare by any terms; since they are not producing or consuming anything themselves and are rather just selling something that is already there.

Moreover, Groupon thrives because a number of people (mainly small retailers, merchants) are worse off, since they have to suffer the consequences of selling at deep discounts, and it is well documented that these people suffer losses due to a Groupon sale. Small retailers build their customer base mostly on repeat customers. However, with a deeply discounted coupon and non-returning customers, Groupon actually leaves a large number of merchants worse off then they were before. Plus, loss of brand value, and group thinking which leads a lot of people to switch their demand curves and expect the same 'groupon' price for actual items, leads to increased loss of welfare. I guess you can argue that the marginal decrease in the welfare of merchants, is compensated by the marginal increase in the welfare of patrons/customers.

So my point being, at best they might have a net zero effect. In most cases, they probably make someone worse off.