  The cosmological event horizons are observer-dependent, which might bring a
paradox. As an example, in dS$_{2}$ multiverse model there are entanglement
islands in crunching regions encoding the information of regions near future
infinity of inflating or Minkowski bubbles, however, for two observers in
different bubbles, since their island regions overlap, both observers will be
able to get access to the information encoded in the overlapping region,
indicating a violation of no-cloning theorem. In this paper, we present a
different resolution to this paradox. Based on the Petz
$\mathrm{R\acute{e}nyi}$ mutual information, we show that besides the quantum
extremal surfaces there might be another boundary for the island in
corresponding spacetime so that the island regions are bounded by ``division
points" rather than extending to the rest of the entire spacetime. We also
discuss the implications of our result.
