Having cheated on my husband, and since I credit this as part of my path to becoming polyamorous, I must confess I am biased in the argument over whether polyamory is of any use in resolving cheating. If cheating is symptomatic of a grave and incurable narcissism in a partner then certainly polyamory will not resolve anything. However there are other reasons why people cheat.
I think very often one of the true motives behind cheating is treating love as a currency in relationships, and assuming you are poor. I certainly know this to be true of my own relationship before we became polyamorous. Furthermore there is a great deal of insecurity and distrust in relationships where one or both partners cheat.
In most monogamous relationships there is a quite common idea that states that, upon marriage/dating/co-habiting all your romantic love now belongs to your partner.
In this context having another relationship essentially involves you giving your love, which does not belong to you because you are part of a couple, to another person. If love is a currency, then having a second relationship is like buying one partner with your finite measure of love, then taking the love back and buying another with the same currency. Apart from the pain of the implied rejection, there is a great measure of outrage over the fraud implicit in this scenario. Even if this is done by agreement it will be very painful for at least one party in the trio.
In polyamory (assuming it is practiced properly) there is no fraud, and love is not considered a currency. It is rather something of a natural resource like air which everyone is entitled to and which is in abundant supply. It is not considered unusual for two partners to agree to allow one another the freedom to explore other relationships because there is no assumption that you are giving away a scarce resource - your partner's love.
Cheating is often a result of insecurity and distrust. When partners feel insecure and distrust each other, they legislate. Thou shalt not look at another woman (lest you leave me for her). Thou shalt not flirt with another man (lest he be better in bed than me). It all boils down to the desire we all have to be loved and wanted and the fear that when the chips are down there are others who are more lovable than we are. These rules do not make us feel any more secure because they undermine any attempt at building real trust. The simple truth is that in such relationships people do not agree to be true to each other through the execution of free will but through mutual fear of abandonment.
For them, learning about non-monogamy may hold the key to healing an unhealthy relationship dynamic, even if they do not convert to an open relationship.
Society idealises and idolises romantic love. It is treated as if it were an illness we contract, or some disease that we suffer from. Our judgement is expected to be warped, our behaviour ridiculous and childish at times and a whole separate set of rules apply to interactions that involve romantic love as opposed to any other kind of love. "All's fair in love and war" people say. A vast swathe of otherwise unacceptable behaviours (jealousy, rudeness, vengefulness etc.) are excused when love is involved. They defend our right to resolve our insecurities and lack of trust by constructing elaborate structures that restrict our partner's movements, social attachments, finances and even feelings rather than by confronting the issue through communication and negotiation. All in the name of "Love".
How would I say polyamory is an alternative to cheating?
I feel it should be understood by the world that trust is the real currency of relationships and that the communication of needs and expectations is the grease that oils the cogs of coupledom. Furthermore total honesty between partners is only way that any relationship should be conducted whether it is monogamous or polyamorous because real love is not conditional.
Polyamorous people can help by teaching these concepts, which are the pillars upon which we build our open relationships. Those of us who successfully practice polyamory needs must have learned some of these skills, because there is nothing that flies apart as quickly as a polyamorous relationship where people don't communicate, don't trust each other and believe that love is a currency which is in short supply.