What message did the frequent and violent changes in leadership might have sent to t he people of the roman empire

I believe this would send two kinds of messages:

- lack of security: any time new war could be called and people killed, which means that long-term planning was difficult

-weakening of authority: any time other leader could take over and might want to "take revenge" on those supporting the current leader,  which gives people incentive to be very careful in supporting their leaders