Conformist social influence is a double-edged sword when it comes to vaccine promotion. On the one hand, social influence may increase vaccine uptake by reassuring the hesitant about the safety and effectiveness of the vaccine; on the other hand, people may forgo the cost of vaccination when the majority is already vaccinated giving rise to a public goods dilemma. Here, we examine whether available information on the percentage of double-vaccinated people affects COVID-19 vaccination intention among unvaccinated people in Turkey. In an online experiment, we divided participants (n = 1013) into low, intermediate and high social influence conditions, reflecting the government's vaccine promotion messages. We found that social influence did not predict COVID-19 vaccination intention, but psychological reactance and collectivism did. People with higher reactance (intolerance of others telling one what to do and being sceptical of consensus views) had lower vaccination intention, whilst people with higher collectivism (how much a person considers group benefits over individual success) had higher vaccination intention. Our findings suggest that advertising the percentage of double-vaccinated people is not sufficient to trigger a cascade of others getting themselves vaccinated. Diverse promotion strategies reflecting the heterogeneity of individual attitudes could be more effective.