may + perfect

"Which tribe are you?" That's the question which has made the census in Kenya controversial. Tribal divisions are deeply rooted in Kenyan society and many people are proud of their tribe. But after last year's inter-tribal violence in which more than one thousand people were killed, there are those who feel the ethnicity question should have been dropped as part of the effort to promote national healing. Some people say they will simply answer, "I am a Kenyan." The government says all the questions are intended to help the authorities to plan better.
Kenyans may have been encouraged to stay at home and be counted but one of the toughest challenges facing the census officials will be finding Kenya's nomadic pastoralists. Due to an ongoing drought they are travelling further, even crossing international borders.

What does 'may have + perfect' structure mean grammatically here?