In the Middle Ages, and even up to the early twentieth century, most of Europe's executioners were related: the Sansons and Deiblers in France, the Pierrepoints in England, etc. The reason for this was that, it generally not being socially acceptable to, well, kill people, executioners and their children could, generally, only marry other executioners or their children.
The parallels with massively inbred, Hapsburg-style dynasties are obvious- imagine a rather clever but politically inept satirist noting this, and being sentenced by the latter to a meeting with the former; even worse, imagine a dynasty of deranged and deformed executioners- think Texas Chaisaw Massacre with government funding.
In cases where a person has accused another of a crime, but there are no other supporters of the accusation or defenders of the accused, and there is not enough evidence to support one party or the other, the two people involved, or their champions in some cases, must duel in the presence of the local ruler or leader. The loser is assumed to be lying and punished accordingly.