Knock Knock.
Who's there?
Can-we.
Can-we who?
Can-we-join-your-board?
No.

Understandably ill-humored Dillard's (NYSE: DDS) revealed yesterday that a private equity firm intends to nominate four candidates to the company's board. It's the most recent of this investor's moves in regard to the Arkansas-based retailer, which will likely receive more attention from shareholders in light of Dillard's fourth-quarter results.

Barington Capital Group, which owns 5.6% of the outstanding shares, began promoting its own ideas for increasing shareholder value while criticizing Dillard's leadership last July. At that point, shares traded for more than $36. Since then, the stock has been on a steady decline, losing half its value, equal to roughly $1.4 billion.

The strategy Barington proposes is mainly real estate-based, not unlike what Eddie Lampert has done with Sears Holdings (Nasdaq: SHLD). Barington is no newcomer to this type of approach. Success stories including Warnaco (Nasdaq: WRNC) and Pep Boys (NYSE: PBY) suggest that it may have some operational tricks up its sleeve.

While Barington may feel it represents opportunity knocking for Dillard's, the company's not rushing to answer. Since its founding in 1938 by the current CEO's father, Dillard's has been tightly controlled by the family. The Dillard name is on many office doors in the executive suite, and the family controls the Class B shares that elect eight of the board's 12 seats. The retailer is notoriously uncommunicative with investors.

To be fair, until this summer, Dillard's had put together a decent five-year run, and its recent stock slide coincides with a general decline for the retail sector. Its fall is a bit steeper, but that may also be due to Barington drawing attention to the company's governance shortcomings.

Absent unforeseen circumstances, I think Barington is unlikely to gain any effective control of Dillard's. Waging a public-relations war is doubtful to have any impact on the family, and may only serve to further depress the stock price. It's possible the Dillard family may just hole up and wait the whole thing out, suggesting that Barington has the right strategy for the wrong target.

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Fool contributor Steven Renaldi always knocks before entering and does not have a position in any of the companies mentioned. The Fool has a disclosure policy.