On Friday, Cablevision's (NYSE:CVC) controlling Dolan family -- obviously sensing that their October offer for the Cablevision shares they don't already own had become inadequate -- raised the ante in their effort to remove Cablevision from the dwindling ranks of publicly held cable companies. It was a move clearly dictated by the increasing strength of the cable industry, including the Long Island-based Cablevision.

In early October, the Dolans tendered their second offer for the company in two years. At $27, the bid exceeded the stock's closing price on the previous day, Oct. 6, by nearly 13%. But subsequent to that offer, most of the cable multisystems operators, including industry leader Comcast (NASDAQ:CMCSA), the cable unit of Time Warner (NYSE:TWX), and Mediacom (NASDAQ:MCCC), reported strong quarters. That made it increasingly likely that the special committee of the Cablevision board considering the Dolans' proposal would probably find it lacking. The Dolans' new $30 offer values the company at $8.9 billion, representing a 25% premium over the Oct. 6 closing share price. Cablevision closed Thursday at $29.60, indicating that the market was betting on a sweetened offer by the Dolans.

The family owns just more than 22% of the company. But much like many media companies' dual-class share structures, the Dolans control a difficult-to-contest 74% of its voting power. The Dolan family is noteworthy not only for building Cablevision -- which owns Radio City Music Hall, Madison Square Garden, and many of the cable systems (excluding Manhattan's) in the New York metropolitan area -- but also for its members' own internecine squabbling in the past.

The family first attempted to take Cablevision private in 2005, proferring $21 a share in cash for the company's approximately 3 million cable subscribers, along with an approximately $12.50-per-share public market offering price for the other assets, which also include the Rainbow Media programming arm. The complicated nature of the first offer was probably its largest flaw, and it was ultimately rescinded.

If successful, the Dolans' latest offer would cause Cablevision to follow the recent privatizations of cable operators Cox Communications and Insight Communications, leaving the industry with just four publicly owned players. The cable companies enjoyed a strong year in 2006, and expectations this year call for more of the same. For its part, Cablevision weighed in with third-quarter results that included 28.3% year-over-year subscriber growth for its digital video product, and a 22.7% increase in high-speed data customers. The company's per-subscriber revenues also grew by 15%.

Indeed, Cablevision's strong results clearly were both a feather in the Dolans' cap and something of a problem for the family, given that the good news prompted their higher offer. Nevertheless, the success -- or lack thereof -- of the latest offer will be determined quickly, given the looming Wednesday deadline on its acceptance. In the meantime, and in light of the small spread between the current trading price and the family's offer, I'd urge Fools to avoid becoming financially involved in Cablevision.

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Fool contributor David Lee Smith does not own shares in any of the companies mentioned. He welcomes your questions or comments.