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The drip, drip, drip of corruption investigations has the attention of state elected officials.

Illinois politicians, due to their peculiarly unique genetic coding, are mostly impervious to embarrassment. But, as recent events show, they have their limits.

With public officials and politically connected players apparently the targets of multiple public corruption investigations in Chicago, Cook County and the General Assembly in Springfield, the professional political class is concerned about appearances.

That’s part of the reason why Illinois House Speaker Michael Madigan this week took steps to block one of those unappetizing political demonstrations that make politics here so revolting.

Madigan made it clear that he’s opposed to former Chicago state Rep. Luis Arroyo, who recently was charged with bribery and forced to resign under pressure from the legislature, picking his own successor.

Arroyo, the Democratic Party committeeman from Chicago’s 36th Ward, has scheduled a Friday meeting with other ward committeemen in his former legislative district, to choose who will succeed him in the Illinois House. No way, said Madigan.

“Any process that includes the participation of the 36th Ward — whether by direct vote or by proxy — would call the legitimacy of the appointment into question, and the qualifications of their candidate would be challenged by the full Illinois House of Representatives,” Madigan warned.

The speaker is obviously correct that it’s bad form for Arroyo to play any meaningful role in choosing the next representative in the 3rd district. Owing to the criminal charges he faces, Arroyo is especially damaged goods.

His pending criminal case — trying to bribe a member of the Illinois Senate — is bad enough. His arrest coming amid extensive publicity about other pending federal criminal investigations makes it even worse.

At least three members of the Illinois Senate have been charged or are ensnared in criminal investigations. Arroyo is the first House member arrested and charged.

It should not be too long before other names — some prominent and some not — are added to that august list.

That kind of thing is bad for the practitioners of the political trade, and Madigan is doing what he can — he can do a lot — to stop the bleeding.

The question, of course, is how Arroyo and his political cronies will respond to Madigan’s warning to the 36th Ward not to participate in naming Arroyo’s successor as well as his clear threat to retaliate by not seating Arroyo’s choice if they do.

Suffice it to say, Madigan’s message was not well received.

One of Arroyo’s associates, Chicago Alderman Ariel Reboyas, characterized Madigan’s announcement as “an illegal and discriminatory effort to disenfranchise Latino voters” and issued an empty threat to file a lawsuit.

Arroyo called Friday’s meeting “as the Democratic committeeman with the greatest number of weighted votes” in the 3rd District. He and/or his ward politicos could proceed as planned, setting the stage for a showdown with Madigan.

But there’s more than one way to skin a cat. If Arroyo properly manages events from behind the scenes, he can select his successor while appearing to heed Madigan’s warning.

It just depends on how ornery Arroyo is feeling. He’s already made it clear that he feels betrayed by his political friends who forced him out of the Illinois House. He can’t be happy with Madigan now publicly undermining whatever political credibility he has left.

Feelings aside, however, the political reality is that most politicians, if they’re smart, don’t challenge Madigan, particularly when the Speaker is holding all the cards.