We don't have synonyms for cannonism yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are canonist, cannabism and cannonier.
(n) :
(US politics, historical) Dominance over the House of Representatives and its discussions and debates, like that exerted by Joseph Gurney Cannon (1836–1926), Republican politician.
(n) :
(US politics, historical) Dominance over the House of Representatives and its discussions and debates, like that exerted by Joseph Gurney Cannon (1836–1926), Republican politician.