The proper functioning of a search head cluster requires that a majority of all its members be up and running.
This is a consequence of the captain election process. To elect a captain, a majority of all cluster members must agree on a captain. It is important to emphasize that the election requires a majority of all members, not just of the currently running members. If only 50% or less of the members are running, therefore, the cluster cannot elect a captain.
For example, a cluster of seven members needs at least four of those members to be running. Similarly, a cluster of six members also requires that a minimum of four members be running. If only three members, of a six or seven member cluster, are running, they do not constitute a majority and thus cannot elect a captain.
Without a captain, the cluster cannot function properly. The individual search heads will continue to service ad hoc search requests, but they will not coordinate their efforts and they will not run scheduled searches.