In what way might a modified union shop weaken the bargaining power that workers have in a union shop?

A modified union shop means that workers are not required and are not forced to join a union in order to obtain employment, they can though join voluntarily. This the opposite of the regular union where after getting the job they have to join the union. If not enough people join the union they have less power when negotiating with the employer whereas the regular union has more power as everyone is in it.

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