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Notes:
With an iBGP full mesh, all BGP routers would received the three possible paths and RR1 would prefer the path via R2, RR2 would prefer the path via R3 and RR3 would prefer the path via R1.
With Route Reflectors, the situation is more complex because each RR only knows some of the routes since each RR only advertises its best path on the iBGP full mesh with the other Rrs.
RR1 will learn the path via RX from its client R1. RR2 learns the path via RY from its client R2 and RR3 learns the path via RZ from its client R3.
Assume RR1is the first to select its path. It selects the RX path since it only knows this path and advertises it to RR2 and RR3. Upon reception of this advertisement, RR3 compares the path via RZ and the path via RX and prefers the path via RX. RR3 advertises its best path to R3, but R3 still prefers its direct path to RZ.. Note that RR3 does not advertise the path via RZ to the other RRs since this is not its best path.
Now, assume that RR2 selects its best path. It knows the paths via RX (learned from RR1) and RY (learned via R2). The current best path is clearly the path via RY and RR2 advertises this path to RR1 and RR3. Upon reception of this advertisement, RR1 will select again its best path. Now, RR1's best path is clearly the path via RY. Unfortunately, the selection of this path forces RR1 to withdraw the path via RX that it initially advertised. Upon reception of the withdraw message, RR3 will need to select its best path... The RRs will exchange BGP messages forever without reaching a consensus.
For more information about this problem and others, see :
T. Griffin, G. Wilfong, On the correctness of iBGP configuration, Proc. ACM SIGCOMM2002, August 2002
Route Oscillations in I-BGP with Route Reflection. Anindya Basu, Chih-Hao Luke Ong, April Rasala, F.Bruce Shepherd, and Gordon Wilfong. SIGCOMM 2002