People often face the challenge of choosing amongst different options with similar attractiveness, such as when choosing a parliamentary candidate, a movie or buying a product in the supermarket. In order to study the distribution of preferences in such situations, we can consider opinion dynamics (where different options are available as well as the undecided state) in network. In this work, we use two different opinion dynamics: one involving the direct contagion from each site to its neighborhood (rule A) and another where the opinion of each site is defined by the local relative majority (rule B). The contact network topology can have a important effect in the final distribution of opinions. We use the Watts-Strogatz network and, in particular, we are interested in investigating the contribution of the network randomness p in the output of the dynamics. Depending on the structural properties of the network and the initial conditions, the final distribution can be: equipartition of preferences, consensus and situations where indecision is relevant. The role of network randomness is nontrivial: for a small number of opinions, the rules A and B (the latter with synchronous update) present an optimum value of p, where the predominance of a winning opinion is maximal. Moreover, for the plurality rule with asynchronous update, the increase of the number of shortcuts can even promote consensus situations. Furthermore, both dynamics coincide for small disorder of the network, but differ for larger disorder. Also we observe that the number of initiators decreases the value of the winning fraction in all types of dynamics and attenuates the local maximum that appears in the small-world region.