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Link to BMJ I posted 2 months ago
https://www.bmj.com/content/373/bmj.n1112
"A total of 552 984 residential households with 2-10 people where there was at least one case were included. In households where the index case was not vaccinated before testing positive, the study found 96 898 secondary cases from 960 765 household contacts (10.1%).
Meanwhile, in households where the index case received the AstraZeneca vaccine 21 days or more before testing positive, 196 secondary cases were seen in 3424 contacts (5.72%). With the Pfizer vaccine (one dose 21 days or more before testing positive), 371 secondary cases were found in 5939 contacts (6.25%)"
However they are currently looking into the viral load being carried in vaccinated people as delta variant seems to match that of unvax. I'll have to find that link later but it's not conclusive yet.
Edit: mentioned link https://www.medicalnewstoday.com/articles/delta-infection-unvaccinated-and-vaccinated-people-have-similar-levels-of-virus
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Yukirin
While still possible to get it and spread it while vaccinated it is a reduced chance.
So whilst not perfect, a group of vaccinated people socialising would still result in fewer cases than a group of un vaccinated or a mixed group.