for every $V∈I$

$(V,V)∈R$  (symmetric)

for $(V_1,V_2)∈R$

$⇒V_1$ and $V_2$ use their voting right in their general election

$⇒(V_2,V_1)∈R$   (Symmetric)

$(V_1,V_2)∈R,(V_2,V_3)∈R$

$⇒V_1,V_2,V_3$ all three use their voting right in genral election 

$⇒(V_1,V_3)∈R$  (Transitive)