That depends on whether one uses the narrow or the broad definition of the word. The broad one integrates a number of concepts outside of the narrow meaning of voter participation such as basic human rights, gender equality and so on. If one looks at the map here you will notice that there are only a handful of countries in the world that are democratic in the broad sense but nevertheless support the death penalty. None of these are Arabic though. If one's distressed by these results the place to look for an explanation is the vast difference between Jordan and Lebanon which is rather stunning as both countries have a similar history in lawmaking (a mixture of traditions, Islamic and European codes) and are both predominantly Sunni's of the Shafi'i school. There must be some local specific difference in play here. At first I suspected it had to do with the language in which the poll was taken but the link provided by Mandrake makes it clear that the question are put in the local language of the interviewees. Figuring out the origin of this specific difference would go a long way in explaining why there are still such harsh notions present in parts of the Islamic world I think.