Route selection in RIPv2 and RIPng (equal hop count)

Question

How do RIPv2/RIPng select between equal routes? Randomly?

For example, 2 broadcast domains, 5 routers, all running RIPv2 and RIPng. The | pipes represent a switch:

 R01  
     | R02
     | R03 | 
     | R04 |    
           | R05

How does R01 decide between R02/R03/R03?

Commentary: There are no static routes. Timers are the same on each router. There are only two IPv4 and two IPv6 networks.

Answer 1

Cisco routers can load balance across equal-cost routes, but you don't give a router make/model. The RFC for RIPv2, RFC 2453, RIP Version 2, actually discusses equal-cost routes:

If the new metric is the same as the old one, it is simplest to do nothing further (beyond re-initializing the timeout, as specified above); but, there is a heuristic which could be applied. Normally, it is senseless to replace a route if the new route has the same metric as the existing route; this would cause the route to bounce back and forth, which would generate an intolerable number of triggered updates. However, if the existing route is showing signs of timing out, it may be better to switch to an equally-good alternative route immediately, rather than waiting for the timeout to happen. Therefore, if the new metric is the same as the old one, examine the timeout for the existing route. If it is at least halfway to the expiration point, switch to the new route. This heuristic is optional, but highly recommended.