We live in a nation of laws. The whole point of the law is to step in and break the cycle of blood feuds by assuming a monopoly on the use of force.
Giving that perogative back to victims' families goes against that. So no, I can't get behind the idea that victims should decide what to do.
Also, letting victims decide would just introduce another layer of arbitrariness. I've heard of lots of victims' family members who have forgiven their loved ones' killers and do NOT want them executed. Whether you live or die shouldn't depend on whose family you hurt.
Finally, I don't think you can say, "I do not feel like I have any right to [vote on this issue either way]". You live in a democracy. If you vote at all, you are voting for people who will make decisions on this and many other issues, and it's your responsibility to inform yourself as best you can, and make the best choice you can based on your values and your understanding of the facts.