Update the description according to the review comments

Part of #2593

Author: veod32

doc/book/replication/repl_leader_elect.rst

@@ -74,12 +74,17 @@ All the non-leader nodes are called *followers*. The nodes that start a new
 election round are called *candidates*. The elected leader sends heartbeats to
 the non-leader nodes to let them know it is alive.
 
-In case there are no heartbeats for a period set by the :ref:`replication_timeout <cfg_replication-replication_timeout>` option,
+In case there are no heartbeats for the period of :ref:`replication_timeout <cfg_replication-replication_timeout>` * 4,
 a non-leader node starts a new election if the following conditions are met:
 
-*   It has a quorum of connections to other cluster members.
+*   The node has a quorum of connections to other cluster members.
 *   None of these cluster members can see the leader node.
 
+..  note::
+
+    A cluster member considers the leader node to be alive if the member received heartbeats from the leader at least once during the period of ``replication_timeout * 4`,
+    and there are no replication errors (the connection is not broken due to timeout or due to an error).
+
 Terms and votes are persisted by each instance to preserve certain Raft guarantees.
 
 During the election, the nodes prefer to vote for those ones that have the
@@ -127,7 +132,7 @@ Configuration
   Heartbeats sent by an active leader have a timeout after which a new election
   starts. Heartbeats are sent once per <replication_timeout> seconds.
   Default value is ``1``. The leader is considered dead if it hasn't sent any
-  heartbeats for the period of ``<replication_timeout> * 4``.
+  heartbeats for the period of ``replication_timeout * 4``.
 * ``replication_synchro_quorum`` -- reuse of the :ref:`replication_synchro_quorum <cfg_replication-replication_synchro_quorum>`
   option for the purpose of configuring the election quorum. The default value is ``1``,
   meaning that each node becomes a leader immediately after voting for itself.

doc/reference/reference_lua/box_info/election.rst

@@ -20,7 +20,7 @@ box.info.election
 
    *    ``term`` -- current election term.
 
-   *    ``vote`` -- ID of a node the current node votes for. If the value is ``0``, it means the node doesn't vote in the current term.
+   *    ``vote`` -- ID of a node the current node votes for. If the value is ``0``, it means the node hasn't voted in the current term yet.
 
    *    ``leader`` -- leader node ID in the current term. If the value is ``0``, it means the node doesn't know which node is the leader in the current term.